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Andersen M.S.,University of California at Los Angeles | Dahl J.,MOSEK ApS | Vandenberghe L.,University of California at Los Angeles
Mathematical Programming Computation | Year: 2010

We describe an implementation of nonsymmetric interior-point methods for linear cone programs defined by two types of matrix cones: the cone of positive semidefinite matrices with a given chordal sparsity pattern and its dual cone, the cone of chordal sparse matrices that have a positive semidefinite completion. The implementation takes advantage of fast recursive algorithms for evaluating the function values and derivatives of the logarithmic barrier functions for these cones.We present experimental results of two implementations, one of which is based on an augmented system approach, and a comparison with publicly available interior-point solvers for semidefinite programming. © The Author(s) 2010. Source

Friberg H.A.,Technical University of Denmark | Friberg H.A.,MOSEK ApS
Mathematical Programming Computation | Year: 2016

The Conic Benchmark Library is an ongoing community-driven project aiming to challenge commercial and open source solvers on mainstream cone support. In this paper, 121 mixed-integer and continuous second-order cone problem instances have been selected from 11 categories as representative for the instances available online. Since current file formats were found incapable, we embrace the new Conic Benchmark Format as standard for conic optimization. Tools are provided to aid integration of this format with other software packages. © 2015, Springer-Verlag Berlin Heidelberg and The Mathematical Programming Society. Source

Andersen E.D.,MOSEK ApS
Proceedings of the 11th International Symposium on Operational Research in Slovenia, SOR 2011 | Year: 2011

For about 10 years the software package MOSEK has been capable of solving large-scale sparse conic quadratic optimization (CQO) problems. Based on the experience gained with CQO during those 10 years we will present a few important applications of conic quadratic optimization, discuss properties of the CQO problem and give an overview of how MOSEK solve a CQO problem. We will also present numerical results demonstrating the performance of MOSEK on CQO problems and discuss future developments. Source

Santini A.,University of Bologna | Friberg H.A.,MOSEK ApS | Ropke S.,Technical University of Denmark
Engineering Optimization | Year: 2015

This article studies the quay crane scheduling problem with non-crossing constraints, which is an operational problem that arises in container terminals. An enhancement to a mixed integer programming model for the problem is proposed and a new class of valid inequalities is introduced. Computational results show the effectiveness of these enhancements in solving the problem to optimality. © 2014 Taylor & Francis. Source

Jensen T.L.,University of Aalborg | Ostergaard J.,University of Aalborg | Dahl J.,MOSEK ApS | Jensen S.H.,University of Aalborg
European Signal Processing Conference | Year: 2010

In this paper, we consider the design of multiple descriptions (MDs) using sparse decompositions. In a description erasure channel only a subset of the transmitted descriptions is received. The MD problem concerns the design of the descriptions such that they individually approximate the source and furthermore are able to refine each other. In this paper, we form descriptions using convex optimization with l1-norm minimization and Euclidean distortion constraints on the re- constructions and show that with this method we can obtain non-trivial descriptions. We give an algorithm based on recently developed first-order method to the proposed convex problem such that we can solve large-scale instances for image sequences. © EURASIP, 2010. Source

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