MOSEK

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MOSEK

Developer(s)	Mosek ApS

Stable release	10.0

Type	Mathematical optimization
License	Proprietary
Website	www.mosek.com

MOSEK is a software package for the solution of linear, mixed-integer linear, quadratic, mixed-integer quadratic, quadratically constrained, conic and convex nonlinear mathematical optimization problems. The applicability of the solver varies widely and is commonly used for solving problems in areas such as engineering, finance and computer science.

The emphasis in MOSEK is on solving large-scale sparse problems, in particular the interior-point optimizer for linear, conic quadratic (a.k.a. Second-order cone programming) and semi-definite (aka. semidefinite programming), which the software is considerably efficient solving.^{[citation needed]}

A special feature of the solver, is its interior-point optimizer, based on the so-called homogeneous model. This implies that MOSEK can reliably detect a primal and/or dual infeasible status as documented in several published papers.^[1]^[2]^[3]

In addition to the interior-point optimizer MOSEK includes:

Primal and dual simplex optimizer for linear problems.
Mixed-integer optimizer for linear, quadratic and conic problems.

In version 9, Mosek introduced support for exponential and power cones^[4] in its solver. It has interfaces^[5] to the C, C#, Java, MATLAB, Python and R languages. Major modelling systems are made compatible with MOSEK, examples are: AMPL, and GAMS. In 2020 the solver also became available in Wolfram Mathematica.^[6]

In addition Mosek can for instance be used with the popular MATLAB packages CVX, and YALMIP.^[7]

The solver is developed by Mosek ApS, a Danish company established in 1997 by Erling D. Andersen. It has its office located in Copenhagen, the capital of Denmark.

References

^ E. D. Andersen and Y. Ye. A computational study of the homogeneous algorithm for large-scale convex optimization. Computational Optimization and Applications, 10:243–269, 1998
^ E. D. Andersen and K. D. Andersen. The MOSEK interior point optimizer for linear programming: an implementation of the homogeneous algorithm.In H. Frenk, K. Roos, T. Terlaky, and S. Zhang, editors, High Performance Optimization, pages 197–232. Kluwer Academic Publishers, 2000
^ E. D. Andersen, C. Roos, and T. Terlaky. On implementing a primal-dual interior-point method for conic quadratic optimization. Math. Programming, 95(2), February 2003
^ "Optimization Online - A primal-dual interior-point algorithm for nonsymmetric exponential-cone optimization".
^ "Mosek - Documentation".
^ "Get a License for MOSEK—Wolfram Language Documentation". reference.wolfram.com. Retrieved 2021-03-20.
^ MOSEK @ Yalmip homepage

Mathematical optimization software

Data formats

Mathematica
MPS
nl
sol

Modeling tools

Solvers

LP, MILP^∗	APOPT^∗ ANTIGONE^∗ Artelys Knitro^∗ BCP^∗ CLP CBC^∗ CPLEX^∗ FortMP^∗ GCG^∗ GLOP^∗ GLPK/GLPSOL^∗ Gurobi Optimizer^∗ HiGHS^∗ LINDO^∗ Lp_solve LOQO Mathematica MINOS MINTO^∗ MOSEK^∗ NAG SCIP^∗ SoPlex Octeract Engine^∗ SYMPHONY^∗ Xpress Optimizer^∗
QP, MIQP^∗	APOPT^∗ ANTIGONE^∗ Artelys Knitro^∗ CBC^∗ CLP CPLEX^∗ FortMP^∗ HiGHS Gurobi Optimizer^∗ IPOPT LINDO^∗ Mathematica MINOS MOSEK^∗ NAG Octeract Engine^∗ SCIP^∗ Xpress Optimizer^∗
QCP, MIQCP^∗	APOPT^∗ ANTIGONE^∗ Artelys Knitro^∗ CPLEX^∗ Gurobi Optimizer^∗ IPOPT LINDO^∗ Mathematica MINOS MOSEK^∗ NAG SCIP^∗ Octeract Engine^∗ Xpress Optimizer^∗ Xpress NonLinear^∗
SOCP, MISOCP^∗	Artelys Knitro^∗ CPLEX^∗ Gurobi Optimizer^∗ LINDO^∗ LOQO Mathematica MOSEK^∗ NAG SCIP^∗ Xpress Optimizer^∗
SDP, MISDP^∗	Mathematica MOSEK NAG
NLP, MINLP^∗	AOA^∗ APOPT^∗ ANTIGONE^∗ Artelys Knitro^∗ BARON^∗ Couenne^∗ Galahad library Gurobi Optimizer^∗ IPOPT LINDO^∗ LOQO MIDACO^∗ MINOS NAG NLPQLP NPSOL SCIP^∗ SNOPT^∗ Octeract Engine^∗ WORHP Xpress NonLinear^∗
GO	ANTIGONE^∗ BARON Couenne^∗ Mathematica LINDO SCIP Octeract Engine
CP	Artelys Kalis Comet CPLEX CP Optimizer Gecode Mathematica JaCoP Xpress Kalis