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arXiv · 2609.32017

Applications of the Lorentz positive cone in nonconvex quadratic optimization

Samuel Burer·Kurt Anstreicher
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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.

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Samuel Burer, Kurt Anstreicher. 2026-09-25. Applications of the Lorentz positive cone in nonconvex quadratic optimization. https://arxiv.org/abs/2609.32017

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