Parabolic Relaxation for Quadratically-constrained Quadratic Programming -- Part II: Theoretical & Computational Results
Optimization and Control
2022-08-09 v1 Machine Learning
Abstract
In the first part of this work [32], we introduce a convex parabolic relaxation for quadratically-constrained quadratic programs, along with a sequential penalized parabolic relaxation algorithm to recover near-optimal feasible solutions. In this second part, we show that starting from a feasible solution or a near-feasible solution satisfying certain regularity conditions, the sequential penalized parabolic relaxation algorithm convergences to a point which satisfies Karush-Kuhn-Tucker optimality conditions. Next, we present numerical experiments on benchmark non-convex QCQP problems as well as large-scale instances of system identification problem demonstrating the efficiency of the proposed approach.
Cite
@article{arxiv.2208.03625,
title = {Parabolic Relaxation for Quadratically-constrained Quadratic Programming -- Part II: Theoretical & Computational Results},
author = {Ramtin Madani and Mersedeh Ashraphijuo and Mohsen Kheirandishfard and Alper Atamturk},
journal= {arXiv preprint arXiv:2208.03625},
year = {2022}
}
Comments
Submitted for journal publication