MOSEK is a software package for the solution of linear, mixed-integer linear, quadratic, mixed-integer quadratic, quadratically constraint, conic and convex nonlinear mathematical optimization problems. The emphasis in MOSEK is on solving large scale sparse problems. Particularly the interior-point optimizer for linear, conic quadratic (aka. Second-order cone programming) and semi-definite (aka. semidefinite programming) problems is very efficient. A special feature of the MOSEK interior-point optimizer is that it is based on the so-called homogeneous model which implies MOSEK can reliably detect a primal and/or dual infeasible status as documented in several published papers.
Problem types MOSEK can solve:
Semidefinite (Positive semidefinite matrix variables)
Quadratic and quadratically constrained
General convex nonlinear
Mixed integer linear, conic and quadratic
Problem size limited only by the available memory.
Interior-point optimizer with basis identification.
Primal and dual simplex optimizers for linear programming.
Highly efficient presolver for reducing problem size before optimization.
Network-simplex for problems with network flow structure.
Branch&bound&cut algorithm for mixed integer problems.
Strengths of MOSEK
The strong point of MOSEK is its state-of-the-art interior-point optimizer for continous linear, quadratic and conic problems.
The interior-point optimizer is capable of exploiting multiple CPUs/cores. A concurrent optimizer is available that makes it possible to solve one problem with different optimizers simultaneously. The default mixed integer optimizer is parallelized and is run-to-run deterministic.
Other features of MOSEK
Reads and writes industry standard formats such as the MPS and LP formats. Includes tools for infeasibility diagnosis and repair. Sensitivity analysis for linear problems
Updates: official site does not provide any info about changes in this version.