Quadratic Programming (QP)Recommended Downloads:
There are very many good options for convex quadratic programming (QP) in TOMLAB, i.e. problems where the quadratic matris is positive semidefinite. For largescale problems it is problem dependent which is the fastest choice of TOMLAB /CPLEX and TOMLAB /Xpress, or possibly TOMLAB /XA. All three packages include both active set and barrier solvers. Other fast active set algorithm alternatives are SQOPT in TOMLAB /SNOPT, MINOS in TOMLAB /MINOS and BQPD in TOMLAB /MINLP. A barrier solver PDCO is included in the TOMLAB Base Module. KNITRO in TOMLAB /KNITRO is also a barrier solver. Applying general nonlinear programming solvers like SNOPT in TOMLAB /SNOPT and filterSQP in TOMLAB /MINLP has the added advantage that they handle nonconvex QPs and at least finds a local solution to the problem. They could also be an advantage if the QP problem is illconditioned. In one test SNOPT performed best of all solvers for an illconditioned largescale QP. When the QP has a special structure that is possible to utilize doing special coding of matrixvector operations, this is easily done when using the nonlinear solvers PDCO, SNOPT, MINOS and filterSQP. The TOMLAB team can assist in efficient coding of your problem. When solving dense problems, QPOPT in TOMLAB /MINOS is the standard choice, and it also handles nonconvex problems. In the TOMLAB Base Module, qpSolve works well for nonconvex QPs of size 100 or less and QLD handles dense convex QPs. Solver reference:
