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arXiv · 2303.06761

On Exact and Inexact RLT and SDP-RLT Relaxations of Quadratic Programs with Box Constraints

Yuzhou Qiu·E. Alper Yıldırım
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Abstract

Quadratic programs with box constraints involve minimizing a possibly nonconvex quadratic function subject to lower and upper bounds on each variable. This is a well-known NP-hard problem that frequently arises in various applications. We focus on two convex relaxations, namely the RLT (Reformulation-Linearization Technique) relaxation and the SDP-RLT relaxation obtained by adding semidefinite constraints to the RLT relaxation. Both relaxations yield lower bounds on the optimal value of a quadratic program with box constraints. We present complete algebraic descriptions of the set of instances that admit exact RLT relaxations as well as those that admit exact SDP-RLT relaxations. We show that our descriptions can be converted into algorithms for efficiently constructing instances with exact or inexact relaxations.

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Yuzhou Qiu, E. Alper Yıldırım. 2023-03-12. On Exact and Inexact RLT and SDP-RLT Relaxations of Quadratic Programs with Box Constraints. https://arxiv.org/abs/2303.06761

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