I wonder why mosek cannot solve this simple problem to optimality (it reports SLOW_PROGRESS). x-ref [docs] improve the docstring for DUAL_INFEASIBLE by odow · Pull Request #2701 · jump-dev/MathOptInterface.jl · GitHub import JuMP, MosekTools model = JuMP.Model(MosekTools.Optimizer) JuMP.@variable(m…

I did 2 more tests where I add artificial bounds to x. Please take a look at their results import JuMP, Clarabel model = JuMP.Model(Clarabel.Optimizer) JuMP.@variable(model, y); JuMP.@variable(model, x); JuMP.@constraint(model, [0 y; y x] in JuMP.PSDCone()) JuMP.@constraint(model, 0 <= x <= 9) JuM…

What I employ Mosek to solve a feasibility system, its tolerance looks like import JuMP, MosekTools # I used Mosek v10 model = JuMP.Model(MosekTools.Optimizer) JuMP.@variable(model, y); JuMP.@variable(model, x) JuMP.@constraint(model, [x y; y 0] in JuMP.PSDCone()) JuMP.set_upper_bound(x, -0.000) Ju…

This isn’t really a numerical issue. It’s related to a much more fundamental issue: some conic programs do not satisfy strong duality. (This doesn’t happen in an LP; strong duality always holds there). why does Gurobi … named PSDCuts but it do not allow users to model with PSD constraints. Becau…

[image] odow: This doesn’t happen in an LP; strong duality always holds there Actually, it always holds if either one side of the two LP problems is feasible. [image] odow: Gurobi does not support PSD constraints It seems I have a clearer understanding of this: Gurobi’s “PSDCut” is …

Due to their poor performance on this simple test case, I propose to solve it via LP relaxation. The crux, is to introduce a proper artificial bound. After adding about 23 linear cuts, we converge to the global optimal value 0.0. import JuMP, Gurobi, LinearAlgebra function my_eigmin(A) valmin…

The above post is LP-relaxation to the SDP cut. If we reformulate the SDP constraint into y^2 <= 0, We can also approach the problem as follows import JuMP, Gurobi function optimise(model) JuMP.optimize!(model) JuMP.assert_is_solved_and_feasible(model; allow_local = false, dual = true) en…

This should be a final perspective on the troublesome SDP problem proposed by @odow (primal problem) \quad \min_{x, y} \{2y | M \in \mathrm{PSD} \}, where M = [0 y; y x]. The difficulty of this problem lies in the unboundedness of the variable x and y. When I employ the LP relaxation to tackle t…

My guess seems to be correct. [image]

SLOW_PROGRESS or NUMERICAL_ERROR: a simple but nontrivial SDP example, solved with LP relaxation

Specific Domains Optimization (Mathematical)

WalterMadelim May 11, 2025, 10:04am 9

My guess seems to be correct.

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SLOW_PROGRESS or NUMERICAL_ERROR: a simple but nontrivial SDP example, solved with LP relaxation

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