Quadratic factorization heuristics for copositive programming

  • Copositive optimization problems are particular conic programs: optimize linear forms over the copositive cone subject to linear constraints. Every quadratic program with linear constraints can be formulated as a copositive program, even if some of the variables are binary. So this is an NP-hard problem class. While most methods try to approximate the copositive cone from within, we propose a method which approximates this cone from outside. This is achieved by passing to the dual problem, where the feasible set is an affine subspace intersected with the cone of completely positive matrices, and this cone is approximated from within. We consider feasible descent directions in the completely positive cone, and regularized strictly convex subproblems. In essence, we replace the intractable completely positive cone with a nonnegative cone, at the cost of a series of nonconvex quadratic subproblems. Proper adjustment of the regularization parameter results in short steps for the nonconvex quadratic programs. This suggests to approximate their solution by standard linearization techniques. Preliminary numerical results on three different classes of test problems are quite promising.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Immanuel M. Bomze, Florian Jarre, Franz Rendl
DOI:https://doi.org/10.1007/s12532-011-0022-z
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2011
Tag:Software; Theoretical Computer Science
Volume:3
Issue:1
Page Number:21
First Page:37
Last Page:57
Mathematical Programming Computation :MPC 2011 - Issue 1
Verstanden ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.