PreprintarXiv licencearXiv
Applications of the Lorentz positive cone in nonconvex quadratic optimization
Abstract
We consider the Lorentz positive cone of n× m matrices that map the Lorentz cone in Rbbm into the Lorentz cone in Rbbn. 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 Rbbn and Rbbm. 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.
Related
- A Proximal Gradient Method for Nonconvex Nonsmooth Optimization with Applications
- Riemannian ascent--descent for nonconvex nonconcave minimax landscapes: convergence to basin saddle points and applications to distributionally robust optimization
- Disjunctive Submodular Functions: Envelopes and Applications to Inventory and 0-1 Quadratic Optimization
- A method for global minimization of nonconvex quadratic functions
- Dynamical Systems and Nonconvex Quadratic Programs
BibTeX
@misc{burer2026applications,
title = {{Applications of the Lorentz positive cone in nonconvex quadratic optimization}},
author = {Samuel Burer and Kurt Anstreicher},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32017},
eprint = {2609.32017},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32017},
}
RIS
TY - UNPB
TI - Applications of the Lorentz positive cone in nonconvex quadratic optimization
AU - Samuel Burer
AU - Kurt Anstreicher
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.32017
UR - https://arxiv.org/abs/2609.32017
AB - We consider the Lorentz positive cone of n× 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.
ER -