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 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 A second-order cone program (SOCP) is a convex optimization problem of the form :minimize \ f^T x \ :subject to ::\lVert A_i x + b_i \rVert_2 \leq c_i^T x + d_i,\quad i = 1,\dots,m ::Fx = g \ where the problem parameters are f \in \mathbb^n, ...

) and semi-definite (aka.

semidefinite programming Semidefinite programming (SDP) is a subfield of convex optimization concerned with the optimization of a linear objective function (a user-specified function that the user wants to minimize or maximize) over the intersection of the cone of positive ...

), 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. 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 in its solver. It has interfaces to the C, C#,

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MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation ...

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and R languages. Major modelling systems are made compatible with MOSEK, examples are:

AMPL AMPL (A Mathematical Programming Language) is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing (i.e., large-scale optimization and scheduling-type problems). It was developed b ...

, and

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. In 2020 the solver also became available in

Wolfram Mathematica Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimizat ...

. In addition Mosek can for instance be used with the popular MATLAB packages CVX, and YALMIP.MOSEK @ Yalmip homepage
/ref> The solver is developed by Mosek ApS, a Danish company established in 1997 by Erling D. Andersen. It has its office located in

Copenhagen Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan ar ...

, the capital of

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References

Mathematical optimization software Numerical software {{compsci-stub