Linear Programming Relaxations of Quadratically Constrained Quadratic Programs
Andrea Qualizza, Pietro Belotti, Francois Margot
TL;DR
This paper explores linear programming techniques to enhance semidefinite relaxations of quadratically constrained quadratic programs, introducing new valid inequalities and demonstrating their effectiveness through computational experiments.
Contribution
It presents novel classes of linear inequalities, such as sparse PSD cuts and principal minors PSD cuts, for improving relaxations of QCQPs.
Findings
New valid inequalities improve relaxation bounds
Sparse PSD cuts enhance computational efficiency
Results show better solution quality on benchmark instances
Abstract
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and principal minors PSD cuts. Computational results based on instances from the literature are presented.
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Taxonomy
TopicsAdvanced Optimization Algorithms Research · Optimization and Mathematical Programming · Multi-Criteria Decision Making