Interplay of non-convex quadratically constrained problems with adjustable robust optimization
- Author(s)
- Immanuel Bomze, Markus Gabl
- Abstract
In this paper we explore convex reformulation strategies for non-convex quadratically constrained optimization problems (QCQPs). First we investigate such reformulations using Pataki's rank theorem iteratively. We show that the result can be used in conjunction with conic optimization duality in order to obtain a geometric condition for the S-procedure to be exact. Based upon known results on the S-procedure, this approach allows for some insight into the geometry of the joint numerical range of the quadratic forms. Then we investigate a reformulation strategy introduced in recent literature for bilinear optimization problems which is based on adjustable robust optimization theory. We show that, via a similar strategy, one can leverage exact reformulation results of QCQPs in order to derive lower bounds for more complicated quadratic optimization problems. Finally, we investigate the use of reformulation strategies in order to derive characterizations of set-copositive matrix cones. Empirical evidence based upon first numerical experiments shows encouraging results.
- Organisation(s)
- Department of Statistics and Operations Research, Research Network Data Science, Research Platform Governance of digital practices, Department of Mathematics
- Journal
- Mathematical Methods of Operations Research
- Volume
- 93
- Pages
- 115-151
- No. of pages
- 37
- ISSN
- 1432-2994
- DOI
- https://doi.org/10.1007/s00186-020-00726-6
- Publication date
- 10-2020
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101015 Operations research
- Keywords
- ASJC Scopus subject areas
- Software, Mathematics(all), Management Science and Operations Research
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/interplay-of-nonconvex-quadratically-constrained-problems-with-adjustable-robust-optimization(ac90c3f6-3a83-4c84-a7f3-d8c91a514b0b).html