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Aras
Jan 2, 2020, 8:01:22 AM1/2/20
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Dear Dr. Lofberg and the community,
I am working on non-convex quadratic programming. CPLEX has been solving this problem for some time now. GUROBI is also solving this problem in version 9.0.
My questions are:
- Gurobi gives me solver not applicable error. Normally with cplex the following works:However, in sdpsettings for Gurobi I couldn't find such an option. In Gurobi's documentation it seems like 'NonConvex' might work: https://www.gurobi.com/documentation/9.0/refman/nonconvex.htmloptimize(Constraint,-Obj,sdpsettings('solver','cplex', 'cplex.optimalitytarget',3));
Is this version not yet updated in Gurobi, or is it available? - In CPLEX the following linear constrained nonconvex quadratic program worksx = sdpvar(2,1);Obj = x(1)^2 + x(2)^2;Constraint = [ abs(x) <= 5];Z = optimize(Constraint,-Obj,sdpsettings('solver','cplex', 'cplex.optimalitytarget',3,'savesolveroutput',1));
however if I change the constraint to norm(x) <= 5 then it gives me an error. I tried x(1)^2 + x(2)^2 <= 5, or norm(x)^2 <= 5. All gives meWarning: Solver not applicable (cplex)
Any idea how I can fix this? It should solve nonconvex quadratic objective and convex quadratic constraints right? Thanks!!
Johan Löfberg
Jan 2, 2020, 8:36:05 AM1/2/20
to YALMIP
cplex with nonconvex quadratic objective does not support the case with SOCP constraints as far as I know (I tried and it gave an error complaining about convexity of objective), i.e. it only supports nonconvex quadratic programming.
Aras
Jan 2, 2020, 8:38:54 AM1/2/20
to YALMIP
Oh, that’s double bad news than. Thank you! Which free solver would you recommend for the norm constrained NCQP problem that I can directly solve via YALMIP?
Johan Löfberg
Jan 2, 2020, 8:44:49 AM1/2/20
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yalmips own bminb
(trying both with 2-norm constraints and squaring them to get convex quadratics. can make big difference in the solution of lower bounds as the first leads to SOCP models while the second leads to relaxaed LP models, but bmibnb is pretty good at strenghening these)
>> x = sdpvar(2,1);Obj = x(1)^2 + x(2)^2;Constraint = [ norm(x) <= 5];Z = optimize(Constraint,-Obj,sdpsettings('solver','bmibnb'))* Starting YALMIP global branch & bound.* Branch-variables : 2* Upper solver : fmincon* Lower solver : GUROBI* LP solver : GUROBI Node Upper Gap(%) Lower Open 1 : -9.861E-32 192.31 -5.000E+01 2 2 : -2.500E+01 64.94 -5.000E+01 3 3 : -2.500E+01 64.94 -5.000E+01 4 4 : -2.500E+01 64.94 -5.000E+01 5 5 : -2.500E+01 64.94 -5.000E+01 6 6 : -2.500E+01 64.94 -5.000E+01 7 7 : -2.500E+01 33.21 -3.536E+01 8 8 : -2.500E+01 33.21 -3.536E+01 9 9 : -2.500E+01 33.21 -3.536E+01 10 10 : -2.500E+01 33.21 -3.536E+01 11 11 : -2.500E+01 33.21 -3.536E+01 12 12 : -2.500E+01 33.21 -3.536E+01 13 13 : -2.500E+01 33.21 -3.536E+01 14 14 : -2.500E+01 33.21 -3.536E+01 15 15 : -2.500E+01 24.19 -3.216E+01 16 16 : -2.500E+01 24.19 -3.216E+01 17 17 : -2.500E+01 24.19 -3.216E+01 18 18 : -2.500E+01 24.19 -3.216E+01 19 19 : -2.500E+01 24.19 -3.216E+01 20 20 : -2.500E+01 24.19 -3.216E+01 21 21 : -2.500E+01 24.19 -3.216E+01 22 22 : -2.500E+01 24.19 -3.216E+01 23 23 : -2.500E+01 9.08 -2.747E+01 24 24 : -2.500E+01 9.08 -2.747E+01 25 25 : -2.500E+01 9.08 -2.747E+01 26 26 : -2.500E+01 9.08 -2.747E+01 27 27 : -2.500E+01 9.08 -2.747E+01 28 28 : -2.500E+01 9.08 -2.747E+01 29 29 : -2.500E+01 9.08 -2.747E+01 30 30 : -2.500E+01 9.08 -2.747E+01 31 31 : -2.500E+01 7.60 -2.705E+01 32 32 : -2.500E+01 7.60 -2.705E+01 33 33 : -2.500E+01 7.60 -2.705E+01 34 34 : -2.500E+01 7.60 -2.705E+01 35 35 : -2.500E+01 7.60 -2.705E+01 36 36 : -2.500E+01 7.60 -2.705E+01 37 37 : -2.500E+01 7.60 -2.705E+01 38 38 : -2.500E+01 7.60 -2.705E+01 39 39 : -2.500E+01 6.53 -2.675E+01 40 40 : -2.500E+01 6.53 -2.675E+01 41 41 : -2.500E+01 6.53 -2.675E+01 42 42 : -2.500E+01 6.53 -2.675E+01 43 43 : -2.500E+01 6.53 -2.675E+01 44 44 : -2.500E+01 6.53 -2.675E+01 45 45 : -2.500E+01 6.53 -2.675E+01 46 46 : -2.500E+01 6.53 -2.675E+01 47 47 : -2.500E+01 3.06 -2.581E+01 48 48 : -2.500E+01 3.06 -2.581E+01 49 49 : -2.500E+01 3.06 -2.581E+01 50 50 : -2.500E+01 3.06 -2.581E+01 51 51 : -2.500E+01 3.06 -2.581E+01 52 52 : -2.500E+01 3.06 -2.581E+01 53 53 : -2.500E+01 3.06 -2.581E+01 54 54 : -2.500E+01 3.06 -2.581E+01 55 55 : -2.500E+01 2.34 -2.562E+01 56 56 : -2.500E+01 2.34 -2.562E+01 57 57 : -2.500E+01 2.34 -2.562E+01 58 58 : -2.500E+01 2.34 -2.562E+01 59 59 : -2.500E+01 2.34 -2.562E+01 60 60 : -2.500E+01 2.34 -2.562E+01 61 61 : -2.500E+01 2.34 -2.562E+01 62 62 : -2.500E+01 2.34 -2.562E+01 63 63 : -2.500E+01 2.03 -2.553E+01 64 64 : -2.500E+01 2.03 -2.553E+01 65 65 : -2.500E+01 2.03 -2.553E+01 66 66 : -2.500E+01 2.03 -2.553E+01 67 67 : -2.500E+01 2.03 -2.553E+01 68 68 : -2.500E+01 2.03 -2.553E+01 69 69 : -2.500E+01 2.03 -2.553E+01 70 70 : -2.500E+01 2.03 -2.553E+01 71 71 : -2.500E+01 1.98 -2.552E+01 72 72 : -2.500E+01 1.98 -2.552E+01 73 73 : -2.500E+01 1.98 -2.552E+01 74 74 : -2.500E+01 1.98 -2.552E+01 75 75 : -2.500E+01 1.98 -2.552E+01 76 76 : -2.500E+01 1.98 -2.552E+01 77 77 : -2.500E+01 1.98 -2.552E+01 78 78 : -2.500E+01 1.98 -2.552E+01 79 79 : -2.500E+01 1.67 -2.544E+01 80 80 : -2.500E+01 1.67 -2.544E+01 81 81 : -2.500E+01 1.67 -2.544E+01 82 82 : -2.500E+01 1.67 -2.544E+01 83 83 : -2.500E+01 1.67 -2.544E+01 84 84 : -2.500E+01 1.67 -2.544E+01 85 85 : -2.500E+01 1.67 -2.544E+01 86 86 : -2.500E+01 1.67 -2.544E+01 87 87 : -2.500E+01 0.99 -2.526E+01 88 * Finished. Cost: -25 Gap: 0.98616* Termination with relative gap satisfied * Timing: 41% spent in upper solver (87 problems solved)* 4% spent in lower solver (91 problems solved)* 31% spent in LP-based domain reduction (714 problems solved)Z = struct with fields:
yalmipversion: '20190425' yalmiptime: 0.6470 solvertime: 7.0150 info: 'Successfully solved (BMIBNB)' problem: 0>> Constraint = [ x'*x <= 25];Z = optimize(Constraint,-Obj,sdpsettings('solver','bmibnb'))* Starting YALMIP global branch & bound.* Branch-variables : 2* Upper solver : fmincon* Lower solver : GUROBI* LP solver : GUROBI Node Upper Gap(%) Lower Open 1 : -2.500E+01 0.00 -2.500E+01 2 Improved solution * Finished. Cost: -25 Gap: 3.8453e-07* Termination with relative gap satisfied * Timing: 39% spent in upper solver (1 problems solved)* 1% spent in lower solver (5 problems solved)* 8% spent in LP-based domain reduction (4 problems solved)Z = struct with fields:
yalmipversion: '20190425' yalmiptime: 0.1900 solvertime: 0.2180 info: 'Successfully solved (BMIBNB)' problem: 0Aras
Jan 2, 2020, 4:54:20 PM1/2/20
to YALMIP
Thanks :) It works!
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