Applications of the Lorentz positive cone in nonconvex quadratic optimization

Samuel Burer; Kurt Anstreicher

doi:10.48550/arxiv.2609.32017

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Applications of the Lorentz positive cone in nonconvex quadratic optimization

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Applications of the Lorentz positive cone in nonconvex quadratic optimization

Samuel Burer and Kurt Anstreicher

arXiv

09/25/2026

DOI: 10.48550/arxiv.2609.32017

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Preprint (Author's original) This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We consider the Lorentz positive cone of$n\times m$matrices that map the Lorentz cone in$\Rbb^m$into the Lorentz cone in$\Rbb^n$ . The Lorentz positive cone and its dual, the cone of Lorentz separable matrices, are shown to provide polynomial-time algorithms for the problem of minimizing a bilinear objective over variables contained in ellipsoids in$\Rbb^n$and$\Rbb^m$ . We also demonstrate how these cones can be used to strengthen SDP relaxations of other nonconvex quadratic optimization problems, including the two-trust-region subproblem.

Mathematics - Optimization and Control

Details

Title: Subtitle: Applications of the Lorentz positive cone in nonconvex quadratic optimization
Creators: Samuel Burer - University of Iowa
Kurt Anstreicher - University of Iowa
Resource Type: Preprint
Publication Details: arXiv
DOI: 10.48550/arxiv.2609.32017
ISSN: 2331-8422
Publisher: arXiv
Language: English
Date posted: 09/25/2026
Academic Unit: Business Analytics
Record Identifier: 9985238183402771

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