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add dual version of the naive SOS problem

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kalmarek 2020-08-27 10:06:02 +02:00
parent df8b177ef5
commit c467a52f83
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1 changed files with 30 additions and 2 deletions
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32
src/sos_sdps.jl
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@ -42,15 +42,41 @@ end
#
###############################################################################
function SOS_problem(X::GroupRingElem, orderunit::GroupRingElem; upper_bound::Float64=Inf)
function SOS_problem_dual(elt::GroupRingElem, order_unit::GroupRingElem;
upper_bound::Float64=Inf)
@assert parent(elt) == parent(order_unit)
RG = parent(elt)
m = Model()
y = @variable(m, y[1:length(elt.coeffs)])
@constraint(m, λ_dual, dot(order_unit.coeffs, y) == 1)
@constraint(m, psd, [y[i] for i in RG.pm] in PSDCone())
if !isinf(upper_bound)
@variable(m, λ_ub_dual)
expr = dot(elt.coeffs, y) + upper_bound*λ_ub_dual
@objective m Min expr
else
@objective m Min dot(elt.coeffs, y)
end
return m
end
function SOS_problem_primal(X::GroupRingElem, orderunit::GroupRingElem;
upper_bound::Float64=Inf)
N = size(parent(X).pm, 1)
m = JuMP.Model();
JuMP.@variable(m, P[1:N, 1:N])
# SP = Symmetric(P)
JuMP.@constraint(m, sdp, P in PSDCone())
if iszero(aug(X)) && iszero(aug(orderunit))
JuMP.@constraint(m, sum(P) == 0)
JuMP.@constraint(m, augmentation, sum(P) == 0)
end
if upper_bound < Inf
@ -71,6 +97,8 @@ function SOS_problem(X::GroupRingElem, orderunit::GroupRingElem; upper_bound::Fl
return m
end
const SOS_problem = SOS_problem_primal
###############################################################################
#
# Symmetrized SDP