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Exploiting aggregate sparsity in second-order cone relaxations for quadratic constrained quadratic programming problems.

Authors :
Sheen, Heejune
Yamashita, Makoto
Source :
Optimization Methods & Software; Apr2022, Vol. 37 Issue 2, p753-771, 19p
Publication Year :
2022

Abstract

Among many approaches to increase the computational efficiency of semidefinite programming (SDP) relaxation for nonconvex quadratic constrained quadratic programming problems (QCQPs), exploiting the aggregate sparsity of the data matrices in the SDP by Fukuda et al. [Exploiting sparsity in semidefinite programming via matrix completion I: General framework, SIAM J. Optim. 11(3) (2001), pp. 647–674] and second-order cone programming (SOCP) relaxation have been popular. In this paper, we exploit the aggregate sparsity of SOCP relaxation of nonconvex QCQPs. Specifically, we prove that exploiting the aggregate sparsity reduces the number of second-order cones in the SOCP relaxation, and that we can simplify the matrix completion procedure by Fukuda et al. in both primal and dual of the SOCP relaxation problem without losing the max-determinant property. For numerical experiments, nonconvex QCQPs from the lattice graph and pooling problem are tested as their SOCP relaxations provide the same optimal value as the SDP relaxations. We demonstrate that exploiting the aggregate sparsity improves the computational efficiency of the SOCP relaxation for the same objective value as the SDP relaxation, thus much larger problems can be handled by the proposed SOCP relaxation than the SDP relaxation. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10556788
Volume :
37
Issue :
2
Database :
Complementary Index
Journal :
Optimization Methods & Software
Publication Type :
Academic Journal
Accession number :
159447574
Full Text :
https://doi.org/10.1080/10556788.2020.1827256