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 |
|---|---|---|---|---|---|---|---|---|---|---|
expMulConstr | optimization (x : ℝ)
minimize (0 : ℝ)
subject to
hx : 0 < x
h : exp (log x * 2) ≤ 1
time_cmd equivalence expMulConstrRed/expMulConstrAuto : expMulConstr := by
pre_dcp
#print expMulConstrAuto | def | Unit.expMulConstr | Test.PreDCP | CvxLean/Test/PreDCP/Unit.lean | [
"CvxLean.Command.Solve",
"CvxLean.Command.Reduction",
"CvxLean.Command.Equivalence",
"CvxLean.Command.Util.TimeCmd",
"CvxLean.Tactic.Basic.ChangeOfVariables",
"CvxLean.Tactic.PreDCP.PreDCP"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
expMulRevObj | optimization (x : ℝ)
minimize ((exp x) ^ (2 : ℝ) : ℝ)
subject to
hx : 0 < x
time_cmd equivalence expMulRevObjRed/expMulRevObjAuto : expMulRevObj := by
pre_dcp
#print expMulRevObjAuto | def | Unit.expMulRevObj | Test.PreDCP | CvxLean/Test/PreDCP/Unit.lean | [
"CvxLean.Command.Solve",
"CvxLean.Command.Reduction",
"CvxLean.Command.Equivalence",
"CvxLean.Command.Util.TimeCmd",
"CvxLean.Tactic.Basic.ChangeOfVariables",
"CvxLean.Tactic.PreDCP.PreDCP"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
expMulRevConstr | optimization (x : ℝ)
minimize (0 : ℝ)
subject to
h : ((exp x) ^ (2 : ℝ)) ≤ 1
time_cmd equivalence expMulRevConstrRed/expMulRevConstrAuto : expMulRevConstr := by
pre_dcp
#print expMulRevConstrAuto | def | Unit.expMulRevConstr | Test.PreDCP | CvxLean/Test/PreDCP/Unit.lean | [
"CvxLean.Command.Solve",
"CvxLean.Command.Reduction",
"CvxLean.Command.Equivalence",
"CvxLean.Command.Util.TimeCmd",
"CvxLean.Tactic.Basic.ChangeOfVariables",
"CvxLean.Tactic.PreDCP.PreDCP"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
expNegEqOneDivObj | optimization (x : ℝ)
minimize (x * exp (-(log x)) : ℝ)
subject to
h : 1 ≤ x
time_cmd equivalence expNegEqOneDivObjRed/expNegEqOneDivObjAuto : expNegEqOneDivObj := by
pre_dcp
#print expNegEqOneDivObjAuto | def | Unit.expNegEqOneDivObj | Test.PreDCP | CvxLean/Test/PreDCP/Unit.lean | [
"CvxLean.Command.Solve",
"CvxLean.Command.Reduction",
"CvxLean.Command.Equivalence",
"CvxLean.Command.Util.TimeCmd",
"CvxLean.Tactic.Basic.ChangeOfVariables",
"CvxLean.Tactic.PreDCP.PreDCP"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
expNegEqOneDivConstr | optimization (x : ℝ)
minimize (0 : ℝ)
subject to
hx : 0 < x
h : x * exp (-(log x)) ≤ x
time_cmd equivalence expNegEqOneDivConstrRed/expNegEqOneDivConstrAuto : expNegEqOneDivConstr := by
pre_dcp
#print expNegEqOneDivConstrAuto | def | Unit.expNegEqOneDivConstr | Test.PreDCP | CvxLean/Test/PreDCP/Unit.lean | [
"CvxLean.Command.Solve",
"CvxLean.Command.Reduction",
"CvxLean.Command.Equivalence",
"CvxLean.Command.Util.TimeCmd",
"CvxLean.Tactic.Basic.ChangeOfVariables",
"CvxLean.Tactic.PreDCP.PreDCP"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
expNegEqOneDivRevObj | optimization (x : ℝ)
minimize (1 / (exp x))
subject to
h : 1 ≤ x
time_cmd equivalence expNegEqOneDivRevObjRed/expNegEqOneDivRevObjAuto : expNegEqOneDivRevObj := by
pre_dcp
#print expNegEqOneDivRevObjAuto | def | Unit.expNegEqOneDivRevObj | Test.PreDCP | CvxLean/Test/PreDCP/Unit.lean | [
"CvxLean.Command.Solve",
"CvxLean.Command.Reduction",
"CvxLean.Command.Equivalence",
"CvxLean.Command.Util.TimeCmd",
"CvxLean.Tactic.Basic.ChangeOfVariables",
"CvxLean.Tactic.PreDCP.PreDCP"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
expNegEqOneDivRevConstr | optimization (x : ℝ)
minimize (0 : ℝ)
subject to
h : 1 / (exp x) ≤ 1
time_cmd equivalence expNegEqOneDivRevConstrRed/expNegEqOneDivRevConstrAuto :
expNegEqOneDivRevConstr := by
pre_dcp
#print expNegEqOneDivRevConstrAuto | def | Unit.expNegEqOneDivRevConstr | Test.PreDCP | CvxLean/Test/PreDCP/Unit.lean | [
"CvxLean.Command.Solve",
"CvxLean.Command.Reduction",
"CvxLean.Command.Equivalence",
"CvxLean.Command.Util.TimeCmd",
"CvxLean.Tactic.Basic.ChangeOfVariables",
"CvxLean.Tactic.PreDCP.PreDCP"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
logMulObj | optimization (x : ℝ)
minimize (- log (x * x) : ℝ)
subject to
hx : 0 < x
time_cmd equivalence logMulObjRed/logMulObjAuto : logMulObj := by
pre_dcp
#print logMulObjAuto | def | Unit.logMulObj | Test.PreDCP | CvxLean/Test/PreDCP/Unit.lean | [
"CvxLean.Command.Solve",
"CvxLean.Command.Reduction",
"CvxLean.Command.Equivalence",
"CvxLean.Command.Util.TimeCmd",
"CvxLean.Tactic.Basic.ChangeOfVariables",
"CvxLean.Tactic.PreDCP.PreDCP"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
logMulConstr | optimization (x : ℝ)
minimize (0 : ℝ)
subject to
hx : 0 < x
h : 1 ≤ log (x * x)
time_cmd equivalence logMulConstrRed/logMulConstrAuto : logMulConstr := by
pre_dcp
#print logMulConstrAuto | def | Unit.logMulConstr | Test.PreDCP | CvxLean/Test/PreDCP/Unit.lean | [
"CvxLean.Command.Solve",
"CvxLean.Command.Reduction",
"CvxLean.Command.Equivalence",
"CvxLean.Command.Util.TimeCmd",
"CvxLean.Tactic.Basic.ChangeOfVariables",
"CvxLean.Tactic.PreDCP.PreDCP"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
logMulRevObj | optimization (x : ℝ)
minimize (exp (log x + log (x + 1)))
subject to
hx : 0 < x
time_cmd equivalence logMulRevObjRed/logMulRevObjAuto : logMulRevObj := by
pre_dcp
#print logMulRevObjAuto | def | Unit.logMulRevObj | Test.PreDCP | CvxLean/Test/PreDCP/Unit.lean | [
"CvxLean.Command.Solve",
"CvxLean.Command.Reduction",
"CvxLean.Command.Equivalence",
"CvxLean.Command.Util.TimeCmd",
"CvxLean.Tactic.Basic.ChangeOfVariables",
"CvxLean.Tactic.PreDCP.PreDCP"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
logMulRevConstr | optimization (x : ℝ)
minimize (0 : ℝ)
subject to
hx : 0 < x
h : exp (log x + log (x + 1)) ≤ 1
time_cmd equivalence logMulRevConstrRed/logMulRevConstrAuto : logMulRevConstr := by
pre_dcp
#print logMulRevConstrAuto | def | Unit.logMulRevConstr | Test.PreDCP | CvxLean/Test/PreDCP/Unit.lean | [
"CvxLean.Command.Solve",
"CvxLean.Command.Reduction",
"CvxLean.Command.Equivalence",
"CvxLean.Command.Util.TimeCmd",
"CvxLean.Tactic.Basic.ChangeOfVariables",
"CvxLean.Tactic.PreDCP.PreDCP"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
logDivObj | optimization (x : ℝ)
minimize (log ((exp x) / x) : ℝ)
subject to
hx : 0 < x
time_cmd equivalence logDivObjRed/logDivObjAuto : logDivObj := by
pre_dcp
#print logDivObjAuto | def | Unit.logDivObj | Test.PreDCP | CvxLean/Test/PreDCP/Unit.lean | [
"CvxLean.Command.Solve",
"CvxLean.Command.Reduction",
"CvxLean.Command.Equivalence",
"CvxLean.Command.Util.TimeCmd",
"CvxLean.Tactic.Basic.ChangeOfVariables",
"CvxLean.Tactic.PreDCP.PreDCP"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
logDivConstr | optimization (x : ℝ)
minimize (0 : ℝ)
subject to
hx : 0 < x
h : log ((exp x) / x) ≤ 1
time_cmd equivalence logDivConstrRed/logDivConstrAuto : logDivConstr := by
pre_dcp
#print logDivConstrAuto | def | Unit.logDivConstr | Test.PreDCP | CvxLean/Test/PreDCP/Unit.lean | [
"CvxLean.Command.Solve",
"CvxLean.Command.Reduction",
"CvxLean.Command.Equivalence",
"CvxLean.Command.Util.TimeCmd",
"CvxLean.Tactic.Basic.ChangeOfVariables",
"CvxLean.Tactic.PreDCP.PreDCP"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
logDivRevObj | optimization (x : ℝ)
minimize (- (log (x ^ (2 : ℝ)) - log x))
subject to
hx : 0 < x
time_cmd equivalence logDivRevObjRed/logDivRevObjAuto : logDivRevObj := by
pre_dcp
#print logDivRevObjAuto | def | Unit.logDivRevObj | Test.PreDCP | CvxLean/Test/PreDCP/Unit.lean | [
"CvxLean.Command.Solve",
"CvxLean.Command.Reduction",
"CvxLean.Command.Equivalence",
"CvxLean.Command.Util.TimeCmd",
"CvxLean.Tactic.Basic.ChangeOfVariables",
"CvxLean.Tactic.PreDCP.PreDCP"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
logDivRevConstr | optimization (x : ℝ)
minimize (0 : ℝ)
subject to
hx : 0 < x
h : - (log (x ^ (2 : ℝ)) - log x) ≤ 1
time_cmd equivalence logDivRevConstrRed/logDivRevConstrAuto : logDivRevConstr := by
pre_dcp
#print logDivRevConstrAuto | def | Unit.logDivRevConstr | Test.PreDCP | CvxLean/Test/PreDCP/Unit.lean | [
"CvxLean.Command.Solve",
"CvxLean.Command.Reduction",
"CvxLean.Command.Equivalence",
"CvxLean.Command.Util.TimeCmd",
"CvxLean.Tactic.Basic.ChangeOfVariables",
"CvxLean.Tactic.PreDCP.PreDCP"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
expLogObj | optimization (x : ℝ)
minimize (exp (log x) : ℝ)
subject to
hx : 0 < x
time_cmd equivalence expLogObjRed/expLogObjAuto : expLogObj := by
pre_dcp
#print expLogObjAuto | def | Unit.expLogObj | Test.PreDCP | CvxLean/Test/PreDCP/Unit.lean | [
"CvxLean.Command.Solve",
"CvxLean.Command.Reduction",
"CvxLean.Command.Equivalence",
"CvxLean.Command.Util.TimeCmd",
"CvxLean.Tactic.Basic.ChangeOfVariables",
"CvxLean.Tactic.PreDCP.PreDCP"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
expLogConstr | optimization (x : ℝ)
minimize (0 : ℝ)
subject to
hx : 0 < x
h : exp (log x) ≤ 1
time_cmd equivalence expLogConstrRed/expLogConstrAuto : expLogConstr := by
pre_dcp
#print expLogConstrAuto | def | Unit.expLogConstr | Test.PreDCP | CvxLean/Test/PreDCP/Unit.lean | [
"CvxLean.Command.Solve",
"CvxLean.Command.Reduction",
"CvxLean.Command.Equivalence",
"CvxLean.Command.Util.TimeCmd",
"CvxLean.Tactic.Basic.ChangeOfVariables",
"CvxLean.Tactic.PreDCP.PreDCP"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
logExpObj | optimization (x : ℝ)
minimize (log (exp x) : ℝ)
subject to
hx : 0 ≤ x
time_cmd equivalence logExpObjRed/logExpObjAuto : logExpObj := by
pre_dcp
#print logExpObjAuto | def | Unit.logExpObj | Test.PreDCP | CvxLean/Test/PreDCP/Unit.lean | [
"CvxLean.Command.Solve",
"CvxLean.Command.Reduction",
"CvxLean.Command.Equivalence",
"CvxLean.Command.Util.TimeCmd",
"CvxLean.Tactic.Basic.ChangeOfVariables",
"CvxLean.Tactic.PreDCP.PreDCP"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
logExpConstr | optimization (x : ℝ)
minimize (0 : ℝ)
subject to
h : log (exp x) ≤ 1
time_cmd equivalence logExpConstrRed/logExpConstrAuto : logExpConstr := by
pre_dcp
#print logExpConstrAuto | def | Unit.logExpConstr | Test.PreDCP | CvxLean/Test/PreDCP/Unit.lean | [
"CvxLean.Command.Solve",
"CvxLean.Command.Reduction",
"CvxLean.Command.Equivalence",
"CvxLean.Command.Util.TimeCmd",
"CvxLean.Tactic.Basic.ChangeOfVariables",
"CvxLean.Tactic.PreDCP.PreDCP"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
A : ℝ | 1
#real_to_float A | def | A | Test.Solve | CvxLean/Test/Solve/RealToFloat.lean | [
"CvxLean.Lib.Minimization",
"CvxLean.Syntax.OptimizationParam",
"CvxLean.Command.Solve.Float.RealToFloatLibrary"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
B : ℝ | 1
#real_to_float B | def | B | Test.Solve | CvxLean/Test/Solve/RealToFloat.lean | [
"CvxLean.Lib.Minimization",
"CvxLean.Syntax.OptimizationParam",
"CvxLean.Command.Solve.Float.RealToFloatLibrary"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
exp1 | optimization (x : ℝ)
maximize (x)
subject to
h : exp x ≤ 10
solve exp1
#print exp1.conicForm
#eval exp1.status -- "PRIMAL_AND_DUAL_FEASIBLE"
#eval exp1.value -- 2.302585
#eval exp1.solution | def | exp1 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/Exp.lean | [
"CvxLean.Command.Solve"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
exp2 | optimization (x : ℝ)
minimize (exp x)
subject to
h : 10 ≤ x
solve exp2
#print exp2.conicForm
#eval exp2.status -- "PRIMAL_AND_DUAL_FEASIBLE"
#eval exp2.value -- 22026.464907
#eval exp2.solution | def | exp2 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/Exp.lean | [
"CvxLean.Command.Solve"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
linear1 | optimization (x : ℝ)
maximize (7 * x + 1)
subject to
h : 2 * x ≤ 3
solve linear1
#print linear1.conicForm
#eval linear1.status -- "PRIMAL_AND_DUAL_FEASIBLE"
#eval linear1.value -- 11.500000
#eval linear1.solution | def | linear1 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/Linear.lean | [
"CvxLean.Command.Solve"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
linear2 | optimization (x y : ℝ)
minimize 40 * x + 30 * y
subject to
c₁ : 12 ≤ x + y
c₂ : 16 ≤ 2 * x + y | def | linear2 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/Linear.lean | [
"CvxLean.Command.Solve"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
linear2Solution : Solution linear2 | { point := ⟨4, 8⟩,
isOptimal := by
split_ands <;> try norm_num
intros x' y' h_feas
simp [feasible, linear2] at h_feas ⊢
linarith }
solve linear2
#print linear2.conicForm
#eval linear2.status -- "PRIMAL_AND_DUAL_FEASIBLE"
#eval linear2.value -- 400.000000
#eval linear2.solution | def | linear2Solution | Test.Solve.Problems | CvxLean/Test/Solve/Problems/Linear.lean | [
"CvxLean.Command.Solve"
] | [
"linear2"
] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
linear3 | optimization (x : Fin 2 → ℝ)
minimize (5 * (x 0) - 4 * (x 1))
subject to
h₁ : 3 ≤ (x 0) + (x 1)
h₂ : (x 1) ≤ 7 + (x 0)
solve linear3
#print linear3.conicForm
#eval linear3.status -- "PRIMAL_AND_DUAL_FEASIBLE"
#eval linear3.value -- -30.000000
#eval linear3.solution 0 -- -2.000000
#eval l... | def | linear3 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/Linear.lean | [
"CvxLean.Command.Solve"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
linear4 | optimization (x : Fin 5 → ℝ) (y z : ℝ)
minimize (Vec.sum x + 10 * (y + z))
subject to
h₁ : 4.0 ≤ y
h₂ : 2.5 ≤ z
h₃ : y + z ≤ Vec.sum x
solve linear4
#print linear4.conicForm
#eval linear4.status -- "PRIMAL_AND_DUAL_FEASIBLE"
#eval linear4.value -- 71.500000
#eval linear4.soluti... | def | linear4 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/Linear.lean | [
"CvxLean.Command.Solve"
] | [
"Vec.sum"
] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
A5 : Matrix (Fin 4) (Fin 4) ℝ | fun i j =>
(#[#[ 0.51417013, -1.40067196, 0.71943208, 0.58510080]
, #[-0.53401066, 1.65680551, 0.13519183, 0.29269704]
, #[ 0.39224659, -0.61942485, 1.73666095, 2.46240110]
, #[ 1.76713469, 0.61389781, 0.80559111, -0.12640489]][i.val]!)[j.val]! | def | A5 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/Linear.lean | [
"CvxLean.Command.Solve"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
b5 : Fin 4 → ℝ | fun i => #[ 10.56567387, 21.07609985, 23.43361457, 15.14706378][i.val]! | def | b5 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/Linear.lean | [
"CvxLean.Command.Solve"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
c5 : Fin 4 → ℝ | fun i => #[ 0.14794342, -0.19493149, 0.31361829, 1.13959857][i.val]! | def | c5 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/Linear.lean | [
"CvxLean.Command.Solve"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
linear5 | optimization (x : Fin 4 → ℝ)
maximize (c5 ⬝ᵥ x)
subject to
h₁ : A5.mulVec x ≤ b5
h₂ : 0 ≤ x
solve linear5
#print linear5.conicForm
#eval linear5.status -- "PRIMAL_AND_DUAL_FEASIBLE"
#eval linear5.value -- 11.814741
#eval linear5.solution 0 -- 0.000005
#eval linear5.solution 1 -- 10.56996... | def | linear5 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/Linear.lean | [
"CvxLean.Command.Solve"
] | [
"b5",
"c5"
] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
log1 | optimization (x : ℝ)
minimize (x)
subject to
h₁ : 10 ≤ log x
h₂ : 0 < x
solve log1
#print log1.conicForm
#eval log1.status -- "PRIMAL_AND_DUAL_FEASIBLE"
#eval log1.value -- 22026.464907
#eval log1.solution | def | log1 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/Log.lean | [
"CvxLean.Command.Solve"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
log2 | optimization (x : ℝ)
maximize (log x)
subject to
h₁ : x ≤ 10
h₂ : 0 < x
solve log2
#print log2.conicForm
#eval log2.status -- "PRIMAL_AND_DUAL_FEASIBLE"
#eval log2.value -- 2.302585
#eval log2.solution | def | log2 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/Log.lean | [
"CvxLean.Command.Solve"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
logDet1 | optimization (X : Matrix (Fin 2) (Fin 2) ℝ)
minimize (Matrix.trace X)
subject to
c1 : 10 ≤ log X.det
c2 : X.PosDef
solve logDet1
#eval logDet1.status -- "PRIMAL_AND_DUAL_FEASIBLE"
#eval logDet1.value -- 296.826317
#eval logDet1.solution 0 0 -- 148.413156
#eval logDet1.solution 0 1 -- ... | def | logDet1 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/LogDet.lean | [
"CvxLean.Command.Solve"
] | [
"c1"
] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
logDet2 | optimization (X : Matrix (Fin 2) (Fin 2) ℝ)
maximize (log X.det)
subject to
c1 : X.PosDef
c2 : X 0 0 + X 0 1 + X 1 1 ≤ 50
solve logDet2
#print logDet2.conicForm
#eval logDet2.status -- "PRIMAL_AND_DUAL_FEASIBLE"
#eval logDet2.value -- 6.725434
#eval logDet2.solution 0 0 -- 33.336064
... | def | logDet2 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/LogDet.lean | [
"CvxLean.Command.Solve"
] | [
"c1"
] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
A1 : Matrix (Fin 2) (Fin 2) ℝ | fun i j =>
(#[#[23.90853599, 0.40930502]
, #[ 0.79090389, 21.30303590]][i.val]!)[j.val]! | def | SDP.A1 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/SDP.lean | [
"CvxLean.Command.Solve"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
b1 : ℝ | 8.0 | def | SDP.b1 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/SDP.lean | [
"CvxLean.Command.Solve"
] | [
"b1"
] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
C1 : Matrix (Fin 2) (Fin 2) ℝ | fun i j =>
(#[#[0.31561605, 0.97905625]
, #[0.84321261, 0.06878862]][i.val]!)[j.val]! | def | SDP.C1 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/SDP.lean | [
"CvxLean.Command.Solve"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
sdp1 | optimization (X : Matrix (Fin 2) (Fin 2) ℝ)
minimize (Matrix.trace (C1 * X))
subject to
h₁ : Matrix.trace (A1 * X) <= b1
h₂ : Matrix.PosSemidef X
solve sdp1
#print sdp1.conicForm
#eval sdp1.status -- "PRIMAL_AND_DUAL_FEASIBLE"
#eval sdp1.value -- -0.266754
#eval sdp1.solution 0 0 -- ... | def | SDP.sdp1 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/SDP.lean | [
"CvxLean.Command.Solve"
] | [
"b1"
] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
so1 | optimization (x y : ℝ)
maximize sqrt (x - y)
subject to
c1 : y = 2 * x - 3
c2 : x ^ (2 : ℝ) ≤ 2
c3 : 0 ≤ x - y
solve so1
#print so1.conicForm
#eval so1.status -- "PRIMAL_AND_DUAL_FEASIBLE"
#eval so1.value -- 2.101003
#eval so1.solution | def | so1 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/SO.lean | [
"CvxLean.Command.Solve"
] | [
"c1"
] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | |
so2 | optimization (x : ℝ)
minimize (x)
subject to
hx : 1 / 1000 ≤ x
h : exp (-x) ≤ sqrt x
solve so2
#print so2.conicForm
#eval so2.status -- "PRIMAL_AND_DUAL_FEASIBLE"
#eval so2.value -- 0.426303
#eval so2.solution | def | so2 | Test.Solve.Problems | CvxLean/Test/Solve/Problems/SO.lean | [
"CvxLean.Command.Solve"
] | [] | https://github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 |
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