MOSEK

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 (a.k.a. Second-order cone programming) and semi-definite (aka. semidefinite programming). The software is particularly very efficient solving the latter set of problems.

MOSEK
Developer(s)Mosek ApS
Stable release
9.y.x
TypeMathematical optimization
LicenseProprietary
Websitewww.mosek.com

A special feature of the MOSEK interior-point optimizer is that it is 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]

The software 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.

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. The software also provides interfaces[5] to the C, C#, Java and Python languages. Most major modeling systems are made compatible with MOSEK, examples are: AMPL, and GAMS. MOSEK can also be used from popular tools such as MATLAB and the R programming language / software environment. With the latter, an outdated version of package Rmosek is available from the CRAN server, the up-to-date version is provided by Mosek ApS[6]), CVX, and YALMIP.[7]

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. http://www.optimization-online.org/DB_HTML/2019/05/7227.html
  5. https://www.mosek.com/documentation/
  6. http://docs.mosek.com/9.0/rmosek/index.html
  7. MOSEK @ Yalmip homepage



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