Numerical block diagonalization of matrix *-algebras with application to semidefinite programming

Authors:
Etienne de Klerk;Cristian Dobre;Dmitrii V. Ṗasechnik
Affiliations:
Tilburg University, Department of Econometrics and OR, Tilburg, The Netherlands;Tilburg University, Department of Econometrics and OR, Tilburg, The Netherlands;Nanyang Technological University, Division of Mathematical Sciences, SPMS, 21 Nanyang Link, 637371, Singapore, Singapore
Venue:
Mathematical Programming: Series A and B - Special Issue on Cone Programming and its Applications
Year:
2011

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Abstract

Semidefinite programming (SDP) is one of the most active areas in mathematical programming, due to varied applications and the availability of interior point algorithms. In this paper we propose a new pre-processing technique for SDP instances that exhibit algebraic symmetry. We present computational results to show that the solution times of certain SDP instances may be greatly reduced via the new approach.