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use @SDconstraint and SOS_problem_(primal|dual)
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@ -89,7 +89,7 @@ function approximate_by_SOS(sett::Naive,
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isdir(fullpath(sett)) || mkpath(fullpath(sett))
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@info "Creating SDP problem..."
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SDP_problem = SOS_problem(elt, orderunit, upper_bound=sett.upper_bound)
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SDP_problem = SOS_problem_primal(elt, orderunit, upper_bound=sett.upper_bound)
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@info Base.repr(SDP_problem)
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@info "Logging solver's progress into $solverlog"
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@ -141,7 +141,7 @@ function approximate_by_SOS(sett::Symmetrized,
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orbit_data = decimate(orbit_data)
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@info "Creating SDP problem..."
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SDP_problem, varP = SOS_problem(elt, orderunit, orbit_data, upper_bound=sett.upper_bound)
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SDP_problem, varP = SOS_problem_primal(elt, orderunit, orbit_data, upper_bound=sett.upper_bound)
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@info Base.repr(SDP_problem)
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@info "Logging solver's progress into $solverlog"
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@ -43,7 +43,7 @@ end
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###############################################################################
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function SOS_problem_dual(elt::GroupRingElem, order_unit::GroupRingElem;
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upper_bound::Float64=Inf)
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lower_bound::Float64=Inf)
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@assert parent(elt) == parent(order_unit)
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RG = parent(elt)
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@ -54,9 +54,10 @@ function SOS_problem_dual(elt::GroupRingElem, order_unit::GroupRingElem;
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@constraint(m, λ_dual, dot(order_unit.coeffs, y) == 1)
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@constraint(m, psd, [y[i] for i in RG.pm] in PSDCone())
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if !isinf(upper_bound)
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if !isinf(lower_bound)
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@variable(m, λ_ub_dual)
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expr = dot(elt.coeffs, y) + upper_bound*λ_ub_dual
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expr = dot(elt.coeffs, y) + lower_bound*λ_ub_dual
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# @constraint m expr >= lower_bound
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@objective m Min expr
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else
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@objective m Min dot(elt.coeffs, y)
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@ -73,7 +74,7 @@ function SOS_problem_primal(X::GroupRingElem, orderunit::GroupRingElem;
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JuMP.@variable(m, P[1:N, 1:N])
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# SP = Symmetric(P)
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JuMP.@constraint(m, sdp, P in PSDCone())
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JuMP.@SDconstraint(m, sdp, P >= 0)
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if iszero(aug(X)) && iszero(aug(orderunit))
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JuMP.@constraint(m, augmentation, sum(P) == 0)
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@ -97,15 +98,13 @@ function SOS_problem_primal(X::GroupRingElem, orderunit::GroupRingElem;
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return m
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end
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const SOS_problem = SOS_problem_primal
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###############################################################################
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#
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# Symmetrized SDP
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#
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###############################################################################
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function SOS_problem(X::GroupRingElem, orderunit::GroupRingElem, data::OrbitData; upper_bound::Float64=Inf)
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function SOS_problem_primal(X::GroupRingElem, orderunit::GroupRingElem, data::OrbitData; upper_bound::Float64=Inf)
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Ns = size.(data.Uπs, 2)
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m = JuMP.Model();
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@ -113,7 +112,7 @@ function SOS_problem(X::GroupRingElem, orderunit::GroupRingElem, data::OrbitData
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for (k,s) in enumerate(Ns)
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Ps[k] = JuMP.@variable(m, [1:s, 1:s])
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JuMP.@constraint(m, Ps[k] in PSDCone())
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JuMP.@SDconstraint(m, Ps[k] >= 0)
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end
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if upper_bound < Inf
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@ -100,7 +100,7 @@ end
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end
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function check_positivity(elt, Δ, orbit_data, upper_bound, warm=nothing; with_solver=with_SCS(20_000, accel=10))
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SDP_problem, varP = PropertyT.SOS_problem(elt, Δ, orbit_data; upper_bound=upper_bound)
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SDP_problem, varP = PropertyT.SOS_problem_primal(elt, Δ, orbit_data; upper_bound=upper_bound)
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status, warm = PropertyT.solve(SDP_problem, with_solver, warm);
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Base.Libc.flush_cstdio()
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