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Add QCQP to polynomial optimization example #318

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Add QCQP to polynomial optimization example #318

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bf89589
Add QCQP to polynomial optimization example
blegat Sep 17, 2023
d2f4ee4
Fixes
blegat Sep 19, 2023
5c11f0d
Fix
blegat Sep 24, 2023
9b01262
Use released PolyJuMP
blegat Dec 6, 2023
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3 changes: 3 additions & 0 deletions docs/Project.toml
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Original file line number Diff line number Diff line change
@@ -1,4 +1,5 @@
[deps]
Alpine = "07493b3f-dabb-5b16-a503-4139292d7dd4"
BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
CSDP = "0a46da34-8e4b-519e-b418-48813639ff34"
Clarabel = "61c947e1-3e6d-4ee4-985a-eec8c727bd6e"
Expand All @@ -10,6 +11,7 @@ Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
Dualization = "191a621a-6537-11e9-281d-650236a99e60"
DynamicPolynomials = "7c1d4256-1411-5781-91ec-d7bc3513ac07"
GroupsCore = "d5909c97-4eac-4ecc-a3dc-fdd0858a4120"
HiGHS = "87dc4568-4c63-4d18-b0c0-bb2238e4078b"
HomotopyContinuation = "f213a82b-91d6-5c5d-acf7-10f1c761b327"
ImplicitPlots = "55ecb840-b828-11e9-1645-43f4a9f9ace7"
Ipopt = "b6b21f68-93f8-5de0-b562-5493be1d77c9"
Expand All @@ -22,6 +24,7 @@ MultivariateBases = "be282fd4-ad43-11e9-1d11-8bd9d7e43378"
MultivariateMoments = "f4abf1af-0426-5881-a0da-e2f168889b5e"
MultivariatePolynomials = "102ac46a-7ee4-5c85-9060-abc95bfdeaa3"
MutableArithmetics = "d8a4904e-b15c-11e9-3269-09a3773c0cb0"
Pavito = "cd433a01-47d1-575d-afb7-6db927ee8d8f"
PermutationGroups = "8bc5a954-2dfc-11e9-10e6-cd969bffa420"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PolyJuMP = "ddf597a6-d67e-5340-b84c-e37d84115374"
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33 changes: 32 additions & 1 deletion docs/src/tutorials/Polynomial Optimization/polynomial_optimization.jl
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Expand Up @@ -35,7 +35,7 @@ model = Model(Ipopt.Optimizer)
@variable(model, a >= 0)
@variable(model, b >= 0)
@constraint(model, a + b >= 1)
@NLobjective(model, Min, a^3 - a^2 + 2a*b - b^2 + b^3)
@objective(model, Min, a^3 - a^2 + 2a*b - b^2 + b^3)
optimize!(model)

# As we can see below, the termination status is `LOCALLY_SOLVED` and not of `OPTIMAL`
Expand Down Expand Up @@ -93,6 +93,37 @@ solution_summary(gmodel)
@test value(b) ≈ 0.5 rtol=1e-5 #src
value(a), value(b)

# ## QCQP approach

import Alpine, HiGHS, Ipopt, Pavito
ipopt = optimizer_with_attributes(
Ipopt.Optimizer,
MOI.Silent() => true,
)
highs = optimizer_with_attributes(
HiGHS.Optimizer,
"presolve" => "on",
"log_to_console" => false,
)
pavito = optimizer_with_attributes(
Pavito.Optimizer,
MOI.Silent() => true,
"mip_solver" => highs,
"cont_solver" => ipopt,
"mip_solver_drives" => false,
)
alpine = optimizer_with_attributes(
Alpine.Optimizer,
"nlp_solver" => ipopt,
"mip_solver" => pavito,
)
set_optimizer(model, () -> PolyJuMP.QCQP.Optimizer(MOI.instantiate(alpine)))
optimize!(model)

# We can see that it found the optimal solution

termination_status(model), value(a), value(b)

# ## Sum-of-Squares approach

# We will now see how to find the optimal solution using Sum of Squares Programming.
Expand Down