Cplex failed to solve a SOCP problme, but Cplexd could

GAMS
1

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.

2

GAMS/Cplex reformulates the quadratic constraint before giving it to to Cplex and Cplex can’t recognize this constraint as SOCP anymore. e GAMS/CplexD does a much better job and gives the constraint “as-is” to Cplex. This a “well known” and annoying issue, see http://support.gams.com/solver:the_d_solvers_gams_conoptd_gams_convertd_and_gams_cplexd#gams_cplexd_versus_gams_cplex.

-Michael

3

Hi,
Michael,
many thanks for your answer. But, in the MISOCP problem, why did the Cplex can recognize the cone constraints and solve the problem successfully?

4

Hard to say. But with binary variables Cplex can do more preprocessing and might be able to identify convexity where it can’t do that with continuous variable only. Lot’s of speculation without seeing the entire model.

-Michael

5

Hi
I have the same problem. I 'm using benders to solve a second order conic problem . original problem is MIQCP and is solved using gams/ cplex. when I fix the binary variables in dual subproblem (QCP) in “large size”, it is unbounded even using cplexd.I tried to solve the primal problem utilizing obj function of dual subproblem in optimality cut, but it is not convereged.I’d appreciate if you could guide me through this.

6

Hi, would you be able to share how you modeled it? I am looking to work on a similar problem.