statement stringlengths 1 615 | proof stringlengths 0 8.26k | type stringclasses 11
values | symbolic_name stringlengths 1 64 | library stringclasses 29
values | filename stringclasses 121
values | imports listlengths 0 15 | deps listlengths 0 20 | docstring stringlengths 0 1.5k | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|
fromArray (A : Array (Array (Array Float))) : EncodedMatrixList | Id.run <| do
let mut eml := empty
for (i, ai) in A.data.enum do
for (j, aij) in ai.data.enum do
for (k, aijk) in aij.data.enum do
if j >= k && (aijk > 0 || aijk < 0) then
eml := eml.addEntry (EncodedMatrixListEntry.mk i j k aijk)
return eml | def | CBF.EncodedMatrixList.fromArray | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
EncodedMatrixListListEntry where
i : Nat
j : Nat
k : Nat
l : Nat
value : Float | structure | CBF.EncodedMatrixListListEntry | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | Represents the entry `Aₖₗ` in the `j`-th matrix of the `i`-th list. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
fromIndexAndEncodedMatrixList (i : Nat) (emle : EncodedMatrixListEntry) :
EncodedMatrixListListEntry | EncodedMatrixListListEntry.mk i emle.i emle.j emle.k emle.value | def | CBF.EncodedMatrixListListEntry.fromIndexAndEncodedMatrixList | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
EncodedMatrixListList where
n : Nat
values : List EncodedMatrixListListEntry | structure | CBF.EncodedMatrixListList | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | Represents `C = [L₁, ...]` where each `Lᵢ` is a list of matrices and `n` is the total number of
non-zero entries. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
empty : EncodedMatrixListList | EncodedMatrixListList.mk 0 [] | def | CBF.EncodedMatrixListList.empty | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
isEmpty (emll : EncodedMatrixListList) : Prop | emll.n = 0 | def | CBF.EncodedMatrixListList.isEmpty | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
addEntry (emll : EncodedMatrixListList) (emlle : EncodedMatrixListListEntry) :
EncodedMatrixListList | if emlle.value > 0 || emlle.value < 0 then
EncodedMatrixListList.mk (emll.n + 1) (emll.values.concat emlle)
else emll | def | CBF.EncodedMatrixListList.addEntry | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
stack (eml1 eml2 : EncodedMatrixListList) : EncodedMatrixListList | EncodedMatrixListList.mk (eml1.n + eml2.n) (eml1.values ++ eml2.values) | def | CBF.EncodedMatrixListList.stack | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
fromIndexAndEncodedMatrixList (i : Nat) (eml : EncodedMatrixList) :
EncodedMatrixListList | Id.run <| do
let mut emll := empty
for emle in eml.values do
let emlle := EncodedMatrixListListEntry.fromIndexAndEncodedMatrixList i emle
emll := emll.addEntry emlle
emll | def | CBF.EncodedMatrixListList.fromIndexAndEncodedMatrixList | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
fromArray (A : Array (Array (Array (Array Float)))) :
EncodedMatrixListList | Id.run <| do
let mut emll := empty
for (i, ai) in A.data.enum do
for (j, aij) in ai.data.enum do
for (k, aijk) in aij.data.enum do
for (l, aijkl) in aijk.data.enum do
if k >= l && (aijkl > 0 || aijkl < 0) then
emll := emll.addEntry (EncodedMatrixListListEntry.mk i j k l aijkl... | def | CBF.EncodedMatrixListList.fromArray | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
Problem where
version : Nat
objSense : ObjSense
scalarVariables : ConeProduct
PSDVariables : DimensionList
scalarConstraints : ConeProduct
PSDConstraints : DimensionList
objectivePSDVariablesCoord : EncodedMatrixList
objectiveScalarVariablesCoord : EncodedVector
objectiveShiftCoord : EncodedValue
sc... | structure | CBF.Problem | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | This is the main definition. It represents a full problem in conic benchmark format. The problem
is defined as follows:
min/max g^obj
s.t. g_i ∈ K_i for i ∈ I --> Scalar constraints
G_i ∈ K_i for i ∈ I^PSD --> PSD constraints
x_j ∈ K_j for j ∈ J --> Scalar var... | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
empty : Problem | {
version := 3,
objSense := ObjSense.MIN,
scalarVariables := ConeProduct.empty,
PSDVariables := DimensionList.empty,
scalarConstraints := ConeProduct.empty,
PSDConstraints := DimensionList.empty,
objectivePSDVariablesCoord := EncodedMatrixList.empty,
objectiveScalarVariablesCoord := EncodedVector.empty,... | def | CBF.Problem.empty | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
setVersion (p : Problem) (v : Nat) : Problem | { p with version := v } | def | CBF.Problem.setVersion | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
setObjSense (p : Problem) (os : ObjSense) : Problem | { p with objSense := os } | def | CBF.Problem.setObjSense | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
setScalarVariables (p : Problem) (cp : ConeProduct) : Problem | { p with scalarVariables := cp } | def | CBF.Problem.setScalarVariables | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
setPSDVariables (p : Problem) (dl : DimensionList) : Problem | { p with PSDVariables := dl } | def | CBF.Problem.setPSDVariables | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
setScalarConstraints (p : Problem) (cp : ConeProduct) : Problem | { p with scalarConstraints := cp } | def | CBF.Problem.setScalarConstraints | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
setPSDConstraints (p : Problem) (dl : DimensionList) : Problem | { p with PSDConstraints := dl } | def | CBF.Problem.setPSDConstraints | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
setObjectivePSDVariablesCoord (p : Problem) (eml : EncodedMatrixList) : Problem | { p with objectivePSDVariablesCoord := eml } | def | CBF.Problem.setObjectivePSDVariablesCoord | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
setObjectiveScalarVariablesCoord (p : Problem) (ev : EncodedVector) : Problem | { p with objectiveScalarVariablesCoord := ev } | def | CBF.Problem.setObjectiveScalarVariablesCoord | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
setObjectiveShiftCoord (p : Problem) (ev : EncodedValue) : Problem | { p with objectiveShiftCoord := ev } | def | CBF.Problem.setObjectiveShiftCoord | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
setScalarConstraintsPSDVariablesCoord (p : Problem) (emll : EncodedMatrixListList) : Problem | { p with scalarConstraintsPSDVariablesCoord := emll } | def | CBF.Problem.setScalarConstraintsPSDVariablesCoord | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
setScalarConstraintsScalarVariablesCoord (p : Problem) (em : EncodedMatrix) : Problem | { p with scalarConstraintsScalarVariablesCoord := em } | def | CBF.Problem.setScalarConstraintsScalarVariablesCoord | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
setScalarConstraintsShiftCoord (p : Problem) (ev : EncodedVector) : Problem | { p with scalarConstraintsShiftCoord := ev } | def | CBF.Problem.setScalarConstraintsShiftCoord | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
setPSDConstraintsScalarVariablesCoord (p : Problem) (emll : EncodedMatrixListList) : Problem | { p with PSDConstraintsScalarVariablesCoord := emll } | def | CBF.Problem.setPSDConstraintsScalarVariablesCoord | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
setPSDConstraintsShiftCoord (p : Problem) (eml : EncodedMatrixList) : Problem | { p with PSDConstraintsShiftCoord := eml } | def | CBF.Problem.setPSDConstraintsShiftCoord | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
addScalarVariable (p : Problem) (c : Cone) : Problem | { p with scalarVariables := p.scalarVariables.addCone c } | def | CBF.Problem.addScalarVariable | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
addPSDVariable (p : Problem) (d : Nat) : Problem | { p with PSDVariables := p.PSDVariables.addDimension d } | def | CBF.Problem.addPSDVariable | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
addScalarConstraint (p : Problem) (c : Cone) : Problem | { p with scalarConstraints := p.scalarConstraints.addCone c } | def | CBF.Problem.addScalarConstraint | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
addPSDConstraint (p : Problem) (d : Nat) : Problem | { p with PSDConstraints := p.PSDConstraints.addDimension d } | def | CBF.Problem.addPSDConstraint | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
addScalarConstraintsPSDVariablesCoord (p : Problem) (i : Nat) (eml : EncodedMatrixList) :
Problem | let emll := EncodedMatrixListList.fromIndexAndEncodedMatrixList i eml
{ p with scalarConstraintsPSDVariablesCoord :=
p.scalarConstraintsPSDVariablesCoord.stack emll } | def | CBF.Problem.addScalarConstraintsPSDVariablesCoord | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
addScalarConstraintsScalarVariablesCoord (p : Problem) (i : Nat) (ev : EncodedVector) :
Problem | let em := EncodedMatrix.fromIndexAndEncodedVector i ev
{ p with scalarConstraintsScalarVariablesCoord :=
p.scalarConstraintsScalarVariablesCoord.stack em } | def | CBF.Problem.addScalarConstraintsScalarVariablesCoord | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
addScalarConstraintsShiftCoord (p : Problem) (i : Nat) (v : Float) : Problem | let ev := EncodedVector.fromIndexAndValue i v
{ p with scalarConstraintsShiftCoord :=
p.scalarConstraintsShiftCoord.stack ev} | def | CBF.Problem.addScalarConstraintsShiftCoord | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
addPSDConstraintsScalarVariablesCoord (p : Problem) (i : Nat) (eml : EncodedMatrixList) :
Problem | let emll := EncodedMatrixListList.fromIndexAndEncodedMatrixList i eml
{ p with PSDConstraintsScalarVariablesCoord :=
p.PSDConstraintsScalarVariablesCoord.stack emll } | def | CBF.Problem.addPSDConstraintsScalarVariablesCoord | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
addPSDConstraintsShiftCoord (p : Problem) (i : Nat) (em : EncodedMatrix) : Problem | let eml := EncodedMatrixList.fromIndexAndEncodedMatrix i em
{ p with PSDConstraintsShiftCoord :=
p.PSDConstraintsShiftCoord.stack eml } | def | CBF.Problem.addPSDConstraintsShiftCoord | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
addScalarValuedAffineConstraint (p : Problem) (c : Cone) (Fk : EncodedMatrixList)
(ak : EncodedVector) (bk : Float) : Problem | Id.run <| do
let k := p.scalarConstraints.k
let mut newP := p
newP := newP.addScalarConstraint c
newP := newP.addScalarConstraintsPSDVariablesCoord k Fk
newP := newP.addScalarConstraintsScalarVariablesCoord k ak
newP := newP.addScalarConstraintsShiftCoord k bk
newP | def | CBF.Problem.addScalarValuedAffineConstraint | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
addMatrixValuedAffineConstraint (p : Problem) (d : Nat) (Hk : EncodedMatrixList)
(Dk : EncodedMatrix) : Problem | Id.run <| do
let k := p.PSDConstraints.n
let mut newP := p
newP := newP.addPSDConstraint d
newP := newP.addPSDConstraintsScalarVariablesCoord k Hk
newP := newP.addPSDConstraintsShiftCoord k Dk
newP | def | CBF.Problem.addMatrixValuedAffineConstraint | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBF.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
inferDimension (ty : Expr) : MetaM (List (Nat × Nat)) | match ty.consumeMData with
| .const ``Real _ =>
return [(1, 1)]
| .forallE _ (.app (.const ``Fin _) nExpr) e _ =>
match e with
| .const ``Real _ => do
let n : Nat ← evalExpr Nat (mkConst ``Nat) nExpr
return [(n, 1)]
| .forallE _ (.app (.const ``Fin _) mExpr) (.const ``Real _) _ => do
... | def | CvxLean.inferDimension | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBFOfProblemData.lean | [
"CvxLean.Lib.Math.Data.Real",
"CvxLean.Meta.Minimization",
"CvxLean.Meta.Util.Error",
"CvxLean.Command.Solve.Float.ProblemData",
"CvxLean.Command.Solve.Mosek.CBF"
] | [] | Given thet type of the domain return the dimensions of each component. For example, for
`ℝ × (Fin n → ℝ) × (Matrix (Fin m) (Fin k) ℝ)`, return `[(1, 1), (n, 1), (m, k)]` | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
getTotalDim (minExpr : MinimizationExpr) : MetaM Nat | do
let vars ← decomposeDomainInstantiating minExpr
let mut totalDim := 0
for (_, varTy) in vars do
let dims ← inferDimension varTy
for (n, m) in dims do
totalDim := totalDim + n * m
return totalDim | def | CvxLean.getTotalDim | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBFOfProblemData.lean | [
"CvxLean.Lib.Math.Data.Real",
"CvxLean.Meta.Minimization",
"CvxLean.Meta.Util.Error",
"CvxLean.Command.Solve.Float.ProblemData",
"CvxLean.Command.Solve.Mosek.CBF"
] | [] | Total dimension of a problem. For example, `ℝ × (Fin n → ℝ) × (Matrix (Fin m) (Fin k) ℝ)` has
total dimension `1 + n + mk`. We use this to know how many optimization variables to generate. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
translateCone : ScalarConeType → CBF.ConeType | | ScalarConeType.Zero => CBF.ConeType.LEq
| ScalarConeType.PosOrth => CBF.ConeType.LPos
| ScalarConeType.Exp => CBF.ConeType.EXP
| ScalarConeType.Q => CBF.ConeType.Q
| ScalarConeType.QR => CBF.ConeType.QR | def | CvxLean.CBF.translateCone | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBFOfProblemData.lean | [
"CvxLean.Lib.Math.Data.Real",
"CvxLean.Meta.Minimization",
"CvxLean.Meta.Util.Error",
"CvxLean.Command.Solve.Float.ProblemData",
"CvxLean.Command.Solve.Mosek.CBF"
] | [
"CBF.ConeType"
] | Translate generic cone types from `CvxLean/Command/Solve/Float/ProblemData.lean` to MOSEK
cones. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
groupCones (sections : ScalarAffineSections) (l : List CBF.Cone) : MetaM (List CBF.Cone) | do
let l := l.toArray
let mut res := []
let mut currIdx := 0
for idx in sections.data do
let group := l[currIdx:idx]
if h : group.size > 0 then
let c := group.get ⟨0, h⟩
let coneType := c.type
for c' in group do
if !(c'.type = coneType) then
throwSolveError "only cone... | def | CvxLean.CBF.groupCones | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBFOfProblemData.lean | [
"CvxLean.Lib.Math.Data.Real",
"CvxLean.Meta.Minimization",
"CvxLean.Meta.Util.Error",
"CvxLean.Command.Solve.Float.ProblemData",
"CvxLean.Command.Solve.Mosek.CBF"
] | [
"CBF.Cone"
] | Constraints in non-matrix cones with intrinsic dimension (`𝒦ₑ`, `𝒬ⁿ⁺¹`, and `𝒬ᵣⁿ⁺²`) are
defined by a series of constraints. These need to be grouped appropriately. In
`CvxLean/Command/Solve/Float/Coeffs.lean` we keep track of these groups as "sections". These are
used here to correctly write the problem in CBF. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
ofProblemData (minExpr : MinimizationExpr) (data : ProblemData)
(sections : ScalarAffineSections) : MetaM CBF.Problem | do
let totalDim ← getTotalDim minExpr
let mut cbf := CBF.Problem.empty
cbf := cbf.addScalarVariable (CBF.Cone.mk CBF.ConeType.F totalDim)
if h : data.objective.isSome then
let sa := data.objective.get h
let AEnc := CBF.EncodedMatrixList.fromArray #[sa.A]
let aEnc := CBF.EncodedVector.fromArray sa.... | def | CvxLean.CBF.ofProblemData | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/CBFOfProblemData.lean | [
"CvxLean.Lib.Math.Data.Real",
"CvxLean.Meta.Minimization",
"CvxLean.Meta.Util.Error",
"CvxLean.Command.Solve.Float.ProblemData",
"CvxLean.Command.Solve.Mosek.CBF"
] | [
"CBF.EncodedMatrix.fromArray",
"CBF.EncodedMatrixList.fromArray",
"CBF.EncodedVector.fromArray",
"CBF.Problem",
"CBF.Problem.empty"
] | Convert numerical problem data of a problem into CBF format to be solved by MOSEK. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
mosekBinPath | "" | def | mosekBinPath | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Path.lean | [] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
Summary where
name : String
problemStatus : String
solutionStatus : String
objectiveName : String
primalObjective : Float
dualObjective : Float | structure | Sol.Summary | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Stores general information about the solution, crucially the optimality status of the problem
and the attained values. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
StatusKey
| UN | BS | SB | LL | UL | EQ | IN | inductive | Sol.StatusKey | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Variable status. Following MOSEK's documentation:
UN : Unknown status.
BS : Basic. Not at limit, adjusted to satisfy the constraints.
SB : Superbasic. Not at limit, adjusted to minimize or maximize the objective.
LL : At the lower limit (bound).
UL : At the upper limit (bound).
EQ : Lower limit is identical to upper li... | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
Constraint where
index : Nat
name : String
status : StatusKey
activity : Float
lowerLimit : Option Float
upperLimit : Option Float
dualLower : Option Float
dualUpper : Option Float | structure | Sol.Constraint | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Value of an optimization constraint. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
Variable extends Constraint where
conicDual : Option Float | structure | Sol.Variable | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Value of an optimization variable. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
SymmMatrixVariable where
index : Nat
name : String
I : Nat
J : Nat
primal : Option Float
dual : Option Float | structure | Sol.SymmMatrixVariable | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Value of an entry of and symmetric matrix optimization variable. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
Result where
summary : Summary
constraints : List Constraint
vars : List Variable
symmMatrixVars : List SymmMatrixVariable | structure | Sol.Result | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | All the data in MOSEK's solution file format. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
Response
| success (res : Result) : Response
| failure (code : Nat) : Response | inductive | Sol.Response | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Either a full result or a MOSEK error code. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
ws' : Parsec Unit | fun it => Lean.Parsec.ParseResult.success (skipWs' it) ()
where
skipWs' (it : String.Iterator) : String.Iterator :=
if it.hasNext then
let c := it.curr
if c = '\u0009' ∨ c = '\u000d' ∨ c = '\u0020' then skipWs' it.next else it
else it | def | Sol.Parser.ws' | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Variation of 'ws' not skipping line breaks. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
endOfLine : Parsec Unit | skipChar '\u000a' <|> eof | def | Sol.Parser.endOfLine | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | End of line (or file). | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
char : Parsec Char | asciiLetter <|> hexDigit <|> pchar '_' <|> fail "Invalid character." | def | Sol.Parser.char | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Parse only valid characters. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
string : Parsec String | many1Chars char | def | Sol.Parser.string | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Parse string containing only valid characters as in `char`. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
nat : Parsec Nat | Json.Parser.natMaybeZero | def | Sol.Parser.nat | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Parse a `Nat` using the `JsonNumber` parser. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
float : Parsec Float | fun it₁ =>
match Json.Parser.num it₁ with
| ParseResult.success it₂ res =>
let f := Float.ofScientific res.mantissa.natAbs true res.exponent
ParseResult.success it₂ (if res.mantissa < 0 then -f else f)
| ParseResult.error it₂ err => ParseResult.error it₂ err | def | Sol.Parser.float | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Parse a `Float` using the `JsonNumber` parser. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
optionFloat : Parsec (Option Float) | (some <$> float) <|> (skipString "NONE" *> pure none) | def | Sol.Parser.optionFloat | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Use `float` or return none if the string is `"NONE"`. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
summaryIdentifier (id : String) : Parsec Unit | skipString id *> ws' *> skipChar ':' *> ws' | def | Sol.Parser.summaryIdentifier | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Skip the beginning of a summary line. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
summaryLine (id : String) (p : Parsec α) : Parsec α | summaryIdentifier id *> p <* ws' <* endOfLine | def | Sol.Parser.summaryLine | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Generic function to parse summary lines. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
stringSummaryLine (id : String) : Parsec String | summaryLine id string | def | Sol.Parser.stringSummaryLine | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Specialize `summaryLine` to strings. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
floatSummaryLine (id : String) : Parsec Float | summaryLine id float | def | Sol.Parser.floatSummaryLine | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Specialize `summaryLine` to floats. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
summary : Parsec Summary | Summary.mk <$>
((skipString "NAME" *> ws' *> skipChar ':' *> ws') *> pure "anonymous" <* endOfLine) <*>
stringSummaryLine "PROBLEM STATUS" <*>
stringSummaryLine "SOLUTION STATUS" <*>
stringSummaryLine "OBJECTIVE NAME" <*>
floatSummaryLine "PRIMAL OBJECTIVE" <*>
floatSummaryLine "DUAL OBJECTIVE" <* ... | def | Sol.Parser.summary | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Parse the whole `Sol.summary` section. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
constraintsTitle : Parsec Unit | skipString "CONSTRAINTS" <* ws' <* endOfLine | def | Sol.Parser.constraintsTitle | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Skip the title in the constraints section. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
constraintsHeaders : Parsec Unit | skipString "INDEX" <* ws' <*
skipString "NAME" <* ws' <*
skipString "AT" <* ws' <*
skipString "ACTIVITY" <* ws' <*
skipString "LOWER LIMIT" <* ws' <*
skipString "UPPER LIMIT" <* ws' <*
skipString "DUAL LOWER" <* ws' <*
skipString "DUAL UPPER" <* ws' <* endOfLine | def | Sol.Parser.constraintsHeaders | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Skip the headers in the constraints section. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
statusKey : Parsec StatusKey | (skipString "UN" *> pure StatusKey.UN) <|>
(skipString "BS" *> pure StatusKey.BS) <|>
(skipString "SB" *> pure StatusKey.SB) <|>
(skipString "LL" *> pure StatusKey.LL) <|>
(skipString "UL" *> pure StatusKey.UL) <|>
(skipString "EQ" *> pure StatusKey.EQ) <|>
(skipString "**" *> pure StatusKey.IN) <|>
(fail... | def | Sol.Parser.statusKey | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Parse a `StatusKey`. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
constraintElem (p : Parsec α) : Parsec α | ws' *> p | def | Sol.Parser.constraintElem | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Generic function to parse constraint elements, handling whitespaces. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
constraint : Parsec Constraint | Constraint.mk <$>
constraintElem nat <*>
constraintElem string <*>
constraintElem statusKey <*>
constraintElem float <*>
constraintElem optionFloat <*>
constraintElem optionFloat <*>
constraintElem optionFloat <*>
constraintElem optionFloat <* ws' <* endOfLine | def | Sol.Parser.constraint | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Parse a `Constraint` line. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
constraints : Parsec (List Constraint) | constraintsTitle *>
constraintsHeaders *>
Array.data <$> many constraint | def | Sol.Parser.constraints | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Parse the whole `Sol.Result.constraints` section. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
varsTitle : Parsec Unit | skipString "VARIABLES" <* endOfLine | def | Sol.Parser.varsTitle | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Skip the title in the variables section. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
varsHeaders : Parsec Unit | skipString "INDEX" <* ws' <*
skipString "NAME" <* ws' <*
skipString "AT" <* ws' <*
skipString "ACTIVITY" <* ws' <*
skipString "LOWER LIMIT" <* ws' <*
skipString "UPPER LIMIT" <* ws' <*
skipString "DUAL LOWER" <* ws' <*
skipString "DUAL UPPER" <* ws' <*
(skipString "CONIC DUAL"... | def | Sol.Parser.varsHeaders | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Skip the headers in the variables section. Handle CONIC DUAL case. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
var : Parsec Variable | let noBreakConstraint := Constraint.mk <$>
constraintElem nat <*>
constraintElem string <*>
constraintElem statusKey <*>
constraintElem float <*>
constraintElem optionFloat <*>
constraintElem optionFloat <*>
constraintElem optionFloat <*>
constraintElem optionFloat
... | def | Sol.Parser.var | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Parse a `Variable` line. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
vars : Parsec (List Variable) | varsTitle *>
varsHeaders *>
Array.data <$> many var | def | Sol.Parser.vars | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Parse the whole `Sol.Result.variables` section. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
symmMatrixVarsTitle : Parsec Unit | skipString "SYMMETRIC MATRIX VARIABLES" <* endOfLine | def | Sol.Parser.symmMatrixVarsTitle | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Skip the title in the symmetric matrix variables section. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
symmMatrixVarsHeaders : Parsec Unit | skipString "INDEX" <* ws' <*
skipString "NAME" <* ws' <*
skipString "I" <* ws' <*
skipString "J" <* ws' <*
skipString "PRIMAL" <* ws' <*
skipString "DUAL" <* ws' <* endOfLine | def | Sol.Parser.symmMatrixVarsHeaders | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Skip the headers in the symmetric matrix variables section. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
symmMatrixVar : Parsec SymmMatrixVariable | SymmMatrixVariable.mk <$>
constraintElem nat <*>
constraintElem string <*>
constraintElem nat <*>
constraintElem nat <*>
constraintElem optionFloat <*>
constraintElem optionFloat <* ws' <* endOfLine | def | Sol.Parser.symmMatrixVar | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Parse a `SymmMatrixVariable` line. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
symmMatrixVars : Parsec (List SymmMatrixVariable) | (symmMatrixVarsTitle *>
symmMatrixVarsHeaders *>
Array.data <$> many symmMatrixVar) <|> pure [] | def | Sol.Parser.symmMatrixVars | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Parse the whole `Sol.Result.symmMatrixVariables` section. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
result : Parsec Result | Result.mk <$>
summary <* ws <*>
constraints <* ws <*>
vars <* ws <*>
symmMatrixVars <* ws | def | Sol.Parser.result | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Parse the whole `Sol.Result` object. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
parse (s : String) : Except String Result | match result s.mkIterator with
| Parsec.ParseResult.success _ res => Except.ok res
| Parsec.ParseResult.error it err =>
Except.error s!"Error at offset {it.i.byteIdx}. Error: {err}.}" | def | Sol.Parser.parse | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/Sol.lean | [
"Lean.Data.Parsec",
"Lean.Data.Json.Parser"
] | [] | Parse using `result` and handle errors. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
Variable.toSimpleVarSol (v : Sol.Variable) : SimpleVarSol | { name := v.name,
value := v.activity } | def | CvxLean.Sol.Variable.toSimpleVarSol | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/SolToSolutionData.lean | [
"CvxLean.Meta.Util.Error",
"CvxLean.Command.Solve.Float.SolutionData",
"CvxLean.Command.Solve.Mosek.Sol"
] | [
"Sol.Variable"
] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
SymmMatrixVariable.toSimpleMatrixVarSol (v : Sol.SymmMatrixVariable) :
SimpleMatrixVarSol | { name := v.name,
I := v.I,
J := v.J,
value := v.primal } | def | CvxLean.Sol.SymmMatrixVariable.toSimpleMatrixVarSol | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/SolToSolutionData.lean | [
"CvxLean.Meta.Util.Error",
"CvxLean.Command.Solve.Float.SolutionData",
"CvxLean.Command.Solve.Mosek.Sol"
] | [
"Sol.SymmMatrixVariable"
] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
Result.toSolutionData (sol : Sol.Result) : SolutionData | { status := sol.summary.problemStatus,
varsSols := sol.vars.map Variable.toSimpleVarSol,
matrixVarsSols := sol.symmMatrixVars.map SymmMatrixVariable.toSimpleMatrixVarSol } | def | CvxLean.Sol.Result.toSolutionData | Command.Solve.Mosek | CvxLean/Command/Solve/Mosek/SolToSolutionData.lean | [
"CvxLean.Meta.Util.Error",
"CvxLean.Command.Solve.Float.SolutionData",
"CvxLean.Command.Solve.Mosek.Sol"
] | [
"Sol.Result"
] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
evalTimeCmd : CommandElab | fun stx => match stx with
| `(time_cmd $cmd) => do
let before ← BaseIO.toIO IO.monoMsNow
elabCommand cmd
let after ← BaseIO.toIO IO.monoMsNow
let diff := after - before
dbg_trace s!"Command time: {diff} ms"
| _ => throwUnsupportedSyntax | def | evalTimeCmd | Command.Util | CvxLean/Command/Util/TimeCmd.lean | [
"Lean"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
p₁ | optimization (x y : ℝ)
maximize sqrt (x - y)
subject to
c1 : y = 2 * x - 3
c2 : x ^ (2 : ℝ) ≤ 2
c3 : 0 ≤ x - y
#check p₁
-- Apply DCP transformation and call solver.
solve p₁
#eval p₁.status
#eval p₁.solution
#eval p₁.value | def | LT2024.p₁ | Demos | CvxLean/Demos/LT2024.lean | [
"CvxLean"
] | [
"c1"
] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
p₂ | optimization (x : ℝ)
minimize (x)
subject to
c1 : 1 / 1000 ≤ x
c2 : 1 / sqrt x ≤ exp x
-- solve p₂
-- set_option trace.Meta.debug true
-- Equivalence mode.
equivalence eqv₂/q₂ : p₂ := by
pre_dcp
solve q₂
#print q₂.conicForm
#eval q₂.status
#eval q₂.solution
#eval q₂.value | def | LT2024.p₂ | Demos | CvxLean/Demos/LT2024.lean | [
"CvxLean"
] | [
"c1"
] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
p₃ (Awall Aflr α β γ δ : ℝ) | optimization (h w d : ℝ)
minimize (1 / (h * w * d))
subject to
c1 : 0 < h
c2 : 0 < w
c3 : 0 < d
c4 : 2 * (h * w + h * d) ≤ Awall
c5 : w * d ≤ Aflr
c6 : α ≤ h / w
c7 : h / w ≤ β
c8 : γ ≤ d / w
c9 : d / w ≤ δ
equivalence* eqv₃/q₃ : p₃ 100 10 0.5 2 0.5 2 := by... | def | LT2024.p₃ | Demos | CvxLean/Demos/LT2024.lean | [
"CvxLean"
] | [
"c1",
"c5"
] | Maximizing the volume of a box.
See: https://www.cvxpy.org/examples/dgp/max_volume_box.html | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
p₃.solution | eqv₃.backward_map q₃.solution
#eval p₃.solution | def | LT2024.p₃.solution | Demos | CvxLean/Demos/LT2024.lean | [
"CvxLean"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
h | p₃.solution.1 | def | LT2024.h | Demos | CvxLean/Demos/LT2024.lean | [
"CvxLean"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
w | p₃.solution.2.1 | def | LT2024.w | Demos | CvxLean/Demos/LT2024.lean | [
"CvxLean"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
d | p₃.solution.2.2
#eval h * w * d
#eval 2 * (h * w + h * d) ≤ 100
#eval w * d ≤ 10
#eval 0.5 ≤ h / w
#eval h / w ≤ 2
#eval 0.5 ≤ d / w
#eval d / w ≤ 2 | def | LT2024.d | Demos | CvxLean/Demos/LT2024.lean | [
"CvxLean"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
p | optimization (x y : ℝ)
minimize -2 * x
subject to
c₁ : 0 ≤ x
c₂ : 1 < y
c₃ : log (y - 1) ≤ 2 * sqrt x + 1
c₄ : 3 * x + 5 * y ≤ 10
-- Transform (proving `p ≡ q`).
equivalence* eqv/q : p := by
change_of_variables! (v) (y ↦ v + 1)
change_of_variables! (w) (v ↦ exp w)
remove_constr c... | def | p | Demos | CvxLean/Demos/README.lean | [
"CvxLean"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
covEstimation (n : ℕ) (N : ℕ) (α : ℝ) (y : Fin N → Fin n → ℝ) | optimization (R : Matrix (Fin n) (Fin n) ℝ)
maximize (∏ i, gaussianPdf R (y i))
subject to
c_pos_def : R.PosDef
c_sparse : R⁻¹.abs.sum ≤ α
reduction* red/covEstimationConvex (n : ℕ) (N : ℕ) (α : ℝ) (y : Fin N → Fin n → ℝ) :
covEstimation n N α y := by
-- Change objective function.
reduction_s... | def | CovarianceEstimation.covEstimation | Examples | CvxLean/Examples/CovarianceEstimation.lean | [
"CvxLean"
] | [
"Matrix.PosDef_inv_iff_PosDef",
"Real.inverse_eq_inv",
"gaussianPdf",
"log_prod_gaussianPdf",
"prod_gaussianPdf_pos",
"sum_quadForm"
] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
nₚ : ℕ | 2 | def | CovarianceEstimation.nₚ | Examples | CvxLean/Examples/CovarianceEstimation.lean | [
"CvxLean"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
Nₚ : ℕ | 4 | def | CovarianceEstimation.Nₚ | Examples | CvxLean/Examples/CovarianceEstimation.lean | [
"CvxLean"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
αₚ : ℝ | 1 | def | CovarianceEstimation.αₚ | Examples | CvxLean/Examples/CovarianceEstimation.lean | [
"CvxLean"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
yₚ : Fin Nₚ → Fin nₚ → ℝ | ![![0, 2], ![2, 0], ![-2, 0], ![0, -2]]
solve covEstimationConvex nₚ Nₚ αₚ yₚ
#print covEstimationConvex.conicForm
-- minimize
-- -(-(Nₚ • log (sqrt ((2 * π) ^ nₚ)) + Nₚ • (-Vec.sum t.0 / 2)) +
-- -(↑Nₚ * trace ((covarianceMatrix fun i => yₚ i) * Rᵀ) / 2))
-- subject to
-- _ : Real.nonnegOrthCone (α... | def | CovarianceEstimation.yₚ | Examples | CvxLean/Examples/CovarianceEstimation.lean | [
"CvxLean"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
Rₚ_opt | red.backward_map nₚ Nₚ αₚ.float yₚ.float covEstimationConvex.solution
#eval Rₚ_opt | def | CovarianceEstimation.Rₚ_opt | Examples | CvxLean/Examples/CovarianceEstimation.lean | [
"CvxLean"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
leastSquares {n : ℕ} (a : Fin n → ℝ) | optimization (x : ℝ)
minimize (∑ i, ((a i - x) ^ 2) : ℝ) | def | leastSquares | Examples | CvxLean/Examples/FittingSphere.lean | [
"CvxLean"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
mean {n : ℕ} (a : Fin n → ℝ) : ℝ | (1 / n) * ∑ i, (a i) | def | mean | Examples | CvxLean/Examples/FittingSphere.lean | [
"CvxLean"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
leastSquares_alt_objFun {n : ℕ} (hn : 0 < n) (a : Fin n → ℝ) (x : ℝ) :
(∑ i, ((a i - x) ^ 2)) = n * ((x - mean a) ^ 2 + (mean (a ^ 2) - (mean a) ^ 2)) | by
calc
-- 1) Σ (aᵢ - x)² = Σ (aᵢ² - 2aᵢx + x²)
_ = ∑ i, ((a i) ^ 2 - 2 * (a i) * x + (x ^ 2)) := by
congr; funext i; simp; ring
-- 2) ... = Σ aᵢ² - 2xΣ aᵢ + nx²
_ = ∑ i, ((a i) ^ 2) - 2 * x * ∑ i, (a i) + n * (x ^ 2) := by
rw [sum_add_distrib, sum_sub_distrib, ← sum_mul, ← mul_sum]; simp [sum_const];... | lemma | leastSquares_alt_objFun | Examples | CvxLean/Examples/FittingSphere.lean | [
"CvxLean"
] | [
"mean"
] | It is useful to rewrite the sum of squares in the following way to prove
`leastSquares_optimal_eq_mean`, following Marty Cohen's answer in
https://math.stackexchange.com/questions/2554243. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
leastSquares_optimal_eq_mean {n : ℕ} (hn : 0 < n) (a : Fin n → ℝ) (x : ℝ)
(h : (leastSquares a).optimal x) : x = mean a | by
simp [optimal, feasible, leastSquares] at h
replace h : ∀ y, (x - mean a) ^ 2 ≤ (y - mean a) ^ 2 := by
intros y
have hy := h y
have h_rw_x := leastSquares_alt_objFun hn a x
have h_rw_y := leastSquares_alt_objFun hn a y
simp only [rpow_two] at h_rw_x h_rw_y ⊢
rwa [h_rw_x, h_rw_y, mul_le_m... | lemma | leastSquares_optimal_eq_mean | Examples | CvxLean/Examples/FittingSphere.lean | [
"CvxLean"
] | [
"leastSquares",
"leastSquares_alt_objFun",
"mean"
] | Key result about least squares: `x* = mean a`. | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
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