Optimization Linear Programming Quadratic Programming Unconstrained Optimization Constrained Optimization, Nonlinear Programming Linear Least Squares Constrained Nonlinear Least Squares Box-bounded Global Optimization Global Optimization, costly functions Mixed-Integer Programming Mixed-Integer Quadratic Programming Mixed-Integer Nonlinear Programming Semi-definite Programming

 TOMLAB /SNOPT - SNOPT TOMLAB /MINLP - bqpd TOMLAB /KNITRO

There are very many good options for convex quadratic programming (QP) in TOMLAB, i.e. problems where the quadratic matris is positive semidefinite. For large-scale 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, CONOPT in TOMLAB /CONOPT and filterSQP in TOMLAB /MINLP has the added advantage that they handle non-convex QPs and at least finds a local solution to the problem. They could also be an advantage if the QP problem is ill-conditioned. In one test SNOPT performed best of all solvers for an ill-conditioned large-scale QP. When the QP has a special structure that is possible to utilize doing special coding of matrix-vector operations, this is easily done when using the nonlinear solvers PDCO, SNOPT, MINOS, CONOPT 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 non-convex problems. In the TOMLAB Base Module, qpSolve works well for non-convex QPs of size 100 or less and QLD handles dense convex QPs.

Solver reference:

 TOMLAB /CPLEX TOMLAB /SNOPT - SQOPT TOMLAB /MINOS - MINOS TOMLAB /MINOS - QPOPT TOMLAB /MINLP - filterSQP TOMLAB /CONOPT TOMLAB Base Module - PDCO TOMLAB Base Module - qpSolve TOMLAB Base Module - qld