MOSEK
Developer(s)Mosek ApS
Stable release
10.0
TypeMathematical optimization
LicenseProprietary
Websitewww.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.

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

  1. ↑ 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
  2. ↑ 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
  3. ↑ 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
  4. ↑ "Optimization Online - A primal-dual interior-point algorithm for nonsymmetric exponential-cone optimization".
  5. ↑ "Mosek - Documentation".
  6. ↑ "Get a License for MOSEK—Wolfram Language Documentation". reference.wolfram.com. Retrieved 2021-03-20.
  7. ↑ MOSEK @ Yalmip homepage
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