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| MOSEK | |
|---|---|
| Name | MOSEK |
| Developer | MOSEK ApS |
| Released | 1997 |
| Latest release | 10.x |
| Programming language | C, C++ |
| Operating system | Windows, Linux, macOS |
| Genre | Mathematical optimization solver |
| License | Proprietary |
MOSEK MOSEK is a high-performance commercial mathematical optimization solver used for large-scale conic, quadratic, and linear programming problems. It is employed across research and industry by users from institutions such as CERN, NASA, Goldman Sachs, Morgan Stanley, Siemens, and Shell for applications in finance, engineering, and data science. The software interoperates with ecosystems around Python (programming language), MATLAB, R (programming language), Julia (programming language), and Apache Spark, and competes with solvers like CPLEX, Gurobi, GLPK, CVXOPT, and MOSEK ApS-adjacent tools.
MOSEK implements interior-point and simplex methods optimized for problems modeled with linear programming, quadratic programming, second-order cone programming, semidefinite programming, and mixed-integer variants used in contexts including portfolio optimization, power system operation, signal processing, machine learning, and structural optimization. The solver emphasizes numerical stability and scalability for extremely large sparse instances encountered at facilities such as Lawrence Berkeley National Laboratory, Argonne National Laboratory, and firms like BlackRock and Two Sigma. MOSEK integrates with modeling languages and environments such as AMPL, GAMS, YALMIP, CVX (software), and JuMP.
Development began in the late 1990s by a team that collaborated with academics from institutions like Technical University of Denmark, University of Copenhagen, Stanford University, University of California, Berkeley, and Massachusetts Institute of Technology. Early releases focused on large-scale linear and convex quadratic programming, later adding second-order cone programming support influenced by research from Yale University and Princeton University. Over successive versions MOSEK incorporated algorithms and numerical techniques drawn from work at IBM Research, AT&T Labs, Bell Labs, and academic groups at ETH Zurich, EPFL, University of Cambridge, and University of Oxford. Commercial adoption accelerated following performance comparisons reported alongside CPLEX and Gurobi in benchmarks conducted by NEOS Server and academic studies at Columbia University and University of Chicago.
MOSEK provides solvers for continuous convex optimization and mixed-integer programming, with support for dense and sparse linear algebra backends similar to those used in software at Intel Corporation and NVIDIA-accelerated environments. Capabilities include warm-starts used in sequential quadratic programming workflows, cone modeling compatible with CVXOPT and SCS (splitting conic solver), and advanced presolve routines comparable to those in IBM ILOG CPLEX Optimization Studio. It exposes parameter tuning and callback facilities adopted by practitioners at Goldman Sachs, J.P. Morgan, and Deutsche Bank for bespoke risk models. MOSEK also supports solution polishing and post-optimal analysis used in studies at Cornell University and Imperial College London.
The core architecture combines sparse linear algebra, multi-threaded factorization, and robust interior-point method implementations inspired by foundational work from Karmarkar, Nesterov, and Nemirovski. It uses Cholesky and LDL^T factorizations akin to libraries developed at SuiteSparse and incorporates iterative refinement techniques discussed in publications from SIAM conferences and INFORMS meetings. For mixed-integer programming, branch-and-cut strategies interface with cutting-plane generation similar to methods in COIN-OR projects and modern heuristics influenced by research at University of Waterloo and Technical University of Munich. Parallelism is exploited in ways comparable to implementations at Microsoft Research and Google Research.
MOSEK offers native APIs and bindings for languages and platforms including Python (programming language), MATLAB, R (programming language), Julia (programming language), C#, Java (programming language), and C++. It integrates with modeling systems and workflow tools such as AMPL, GAMS, JuMP, YALMIP, CVX (software), Pyomo, and distributed computing frameworks like Apache Spark and Dask. Enterprise integrations often involve Docker, Kubernetes, and cloud platforms operated by Amazon Web Services, Microsoft Azure, and Google Cloud Platform, enabling deployment in pipelines used by Schneider Electric and ABB Group.
MOSEK is distributed under proprietary licenses with academic and trial tiers similar to commercial models used by Gurobi and CPLEX. Licensing options include per-seat, server, and cloud-based subscriptions adopted by financial institutions such as UBS and energy companies like ExxonMobil. Academic licenses permit use in universities including University of Pennsylvania and University of Toronto for research and teaching. Commercial support and maintenance agreements mirror service offerings from Red Hat and Oracle Corporation for enterprise customers.
MOSEK is applied in quantitative finance for mean-variance optimization practiced at Goldman Sachs and BlackRock, in energy systems optimization at National Grid and E.ON, and in telecommunications network design for firms like Ericsson and Huawei. Performance benchmarks published in academic venues at INFORMS Journal on Computing, Mathematical Programming, and Operations Research Letters compare MOSEK favorably on large convex cone problems versus SCS (splitting conic solver), ECOS, and SDPA. Case studies from Siemens and ABB Group demonstrate speedups in optimal power flow formulations, while machine learning research groups at Carnegie Mellon University and University of Washington leverage MOSEK for support vector machine training and sparse regression tasks.
Category:Optimization software