Linear Programming (LP)

Linear programming problems are solved most efficiently with TOMLAB /GUROBI, TOMLAB /CPLEX and TOMLAB /XA. Problems with millions of variables are possible to solve where the available memory is the limit. These packages include both simplex based algorithms and barrier methods. TOMLAB /CPLEX also includes a special network algorithm. For less time-critical problems, TOMLAB /MINOS is recommended. For LP, the package includes the sparse solver MINOS, and the dense solver LPOPT. Even if MINOS is really an NLP solver, it is designed to be very efficient for LPs and QPs as well, and has been regarded a reliable high-quality solver for more than twenty years. Advanced scaling features and warm-start facilities make it a good choice when solving large sets of LPs and QPs.

Almost all other solvers can be used to solve LPs. Two simplex based large-scale sparse alternatives are SQOPT in TOMLAB /SNOPT, and BQPD in TOMLAB /MINLP. PDCO in the TOMLAB Base Module is a good barrier solver. Simplex based medium-scale LP solvers in the TOMLAB Base Module are lpSolve and the QP solver QLD.