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Refactor KKT #97

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Oct 13, 2023
Merged

Refactor KKT #97

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cb4d50b
Refactor KKT
blegat Oct 12, 2023
72ae07f
Fix format
blegat Oct 12, 2023
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70 changes: 2 additions & 68 deletions src/KKT/KKT.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -125,75 +125,13 @@ function MOI.copy_to(dest::Optimizer, src::MOI.ModelLike)
return MOI.Utilities.default_copy_to(dest, src)
end

function _add_to_system(system, lagrangian, ::SS.FullSpace, ::Bool)
return lagrangian
end

function _add_to_system(
system,
lagrangian,
set::SS.AlgebraicSet,
maximization::Bool,
)
n = SS.nequalities(set)
if iszero(n)
return
end
DynamicPolynomials.@polyvar λ[1:n]
for i in eachindex(λ)
p = SS.equalities(set)[i]
SS.add_equality!(system, p)
if maximization
lagrangian = MA.add_mul!!(lagrangian, λ[i], p)
else
lagrangian = MA.sub_mul!!(lagrangian, λ[i], p)
end
end
return lagrangian
end

function _add_to_system(
system,
lagrangian,
set::SS.BasicSemialgebraicSet,
maximization::Bool,
)
lagrangian = _add_to_system(system, lagrangian, set.V, maximization)
DynamicPolynomials.@polyvar σ[1:PolyJuMP._nineq(set)]
for i in eachindex(σ)
p = SS.inequalities(set)[i]
SS.add_equality!(system, σ[i] * p)
if maximization
lagrangian = MA.add_mul!!(lagrangian, σ[i]^2, p)
else
lagrangian = MA.sub_mul!!(lagrangian, σ[i]^2, p)
end
end
return lagrangian
end

function _square(x::Vector{T}, n) where {T}
return T[(i + n in eachindex(x)) ? x[i] : x[i]^2 for i in eachindex(x)]
end

function _optimize!(model::Optimizer{T}) where {T}
if isnothing(model.options.solver)
system = SS.AlgebraicSet{T,PolyJuMP.PolyType{T}}()
else
I = SS.PolynomialIdeal{T,PolyJuMP.PolyType{T}}()
system = SS.AlgebraicSet(I, model.options.solver)
end
if model.model.objective_sense == MOI.FEASIBILITY_SENSE
lagrangian = MA.Zero()
else
lagrangian = MA.mutable_copy(model.model.objective_function)
end
lagrangian = _add_to_system(
system,
lagrangian,
model.model.set,
model.model.objective_sense == MOI.MAX_SENSE,
)
lagrangian, system =
PolyJuMP.lagrangian_kkt(model.model, model.options.solver)
x = MP.variables(model.model)
if lagrangian isa MA.Zero
model.solutions = [
Expand All @@ -207,10 +145,6 @@ function _optimize!(model::Optimizer{T}) where {T}
model.raw_status = "Lagrangian function is zero so any solution is optimal even if the solver reports a unique solution `0`."
return
end
∇x = MP.differentiate(lagrangian, x)
for p in ∇x
SS.add_equality!(system, p)
end
solutions = nothing
try # We could check `SS.is_zero_dimensional(system)` but that would only work for Gröbner basis based
solutions = collect(system)
Expand Down
75 changes: 75 additions & 0 deletions src/model.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -208,6 +208,7 @@
) where {T}
return true
end

function MOI.set(
model::Model{T},
::MOI.ObjectiveFunction,
Expand All @@ -216,3 +217,77 @@
model.objective_function = _polynomial(model.variables, func)
return
end

function _add_to_system(_, lagrangian, ::SS.FullSpace, ::Bool)
return lagrangian
end

function _add_to_system(
system,
lagrangian,
set::SS.AlgebraicSet,
maximization::Bool,
)
n = SS.nequalities(set)
if iszero(n)
return

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end
DynamicPolynomials.@polyvar λ[1:n]
for i in eachindex(λ)
p = SS.equalities(set)[i]
SS.add_equality!(system, p)
if maximization
lagrangian = MA.add_mul!!(lagrangian, λ[i], p)
else
lagrangian = MA.sub_mul!!(lagrangian, λ[i], p)
end
end
return lagrangian
end

function _add_to_system(
system,
lagrangian,
set::SS.BasicSemialgebraicSet,
maximization::Bool,
)
lagrangian = _add_to_system(system, lagrangian, set.V, maximization)
DynamicPolynomials.@polyvar σ[1:PolyJuMP._nineq(set)]
for i in eachindex(σ)
p = SS.inequalities(set)[i]
SS.add_equality!(system, σ[i] * p)
if maximization
lagrangian = MA.add_mul!!(lagrangian, σ[i]^2, p)
else
lagrangian = MA.sub_mul!!(lagrangian, σ[i]^2, p)
end
end
return lagrangian
end

function lagrangian_kkt(model::Model{T}, solver = nothing) where {T}
if isnothing(solver)
system = SS.AlgebraicSet{T,PolyJuMP.PolyType{T}}()

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else
I = SS.PolynomialIdeal{T,PolyJuMP.PolyType{T}}()
system = SS.AlgebraicSet(I, solver)
end
if model.objective_sense == MOI.FEASIBILITY_SENSE
lagrangian = MA.Zero()
else
lagrangian = MA.mutable_copy(model.objective_function)
end
lagrangian = _add_to_system(
system,
lagrangian,
model.set,
model.objective_sense == MOI.MAX_SENSE,
)
if !(lagrangian isa MA.Zero)
∇x = MP.differentiate(lagrangian, MP.variables(model))
for p in ∇x
SS.add_equality!(system, p)
end
end
return lagrangian, system
end
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