Cone constraints are not convex in SOCP, but convex in MISOCP

Problems with modeling
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feifan
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Cone constraints are not convex in SOCP, but convex in MISOCP

Post by feifan » 2 weeks ago

Hi, all,

I modeled a MISCOP problem with the following second-order cone constraints and this problem can be solved by CPLEX successfully. But, the weird thing is that when I fixed all integer variables as the values obtained, the CPLEX failed to solve the SCOP problem and said that these cone constraints are not convex. However, when I use the cplexd solver, it works. Why did this happen?

%% cone constraints

.. V_s(n)*I_s(L)=g=sqr(P_l(L))+sqr(Q_l(L));
.. V_s(n)*I_sb(B)=g=sqr(P_b(B))+sqr(Q_b(B));

where n, L, B are set, V_s, I_s, I_sb are positive variables, P_l, Q_l, P_b, Q_b are free variables.

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