On global optimization with indefinite quadratics

Marcia Fampa (), Jon Lee () and Wendel Melo
Additional contact information
Marcia Fampa: Universidade Federal do Rio de Janeiro
Jon Lee: University of Michigan
Wendel Melo: Universidade Federal do Rio de Janeiro

EURO Journal on Computational Optimization, 2017, vol. 5, issue 3, No 1, 309-337

Abstract: Abstract We present an algorithmic framework for global optimization problems in which the non-convexity is manifested as an indefinite-quadratic as part of the objective function. Our solution approach consists of applying a spatial branch-and-bound algorithm, exploiting convexity as much as possible, not only convexity in the constraints, but also extracted from the indefinite-quadratic. A preprocessing stage is proposed to split the indefinite-quadratic into a difference of convex quadratic functions, leading to a more efficient spatial branch-and-bound focused on the isolated non-convexity. We investigate several natural possibilities for splitting an indefinite quadratic at the preprocessing stage, and prove the equivalence of some of them. Through computational experiments with our new solver iquad, we analyze how the splitting strategies affect the performance of our algorithm, and find guidelines for choosing amongst them.

Keywords: Global optimization; Indefinite quadratic; Difference of convex functions; Eigendecomposition; Semidefinite programming; Mixed-integer non-linear programming; 90-XX; 90Cxx; 90C26; 90C11; 90C20; 90C22 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://link.springer.com/10.1007/s13675-016-0079-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:eurjco:v:5:y:2017:i:3:d:10.1007_s13675-016-0079-6

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/13675

DOI: 10.1007/s13675-016-0079-6

Access Statistics for this article

EURO Journal on Computational Optimization is currently edited by Martine C. Labbé

More articles in EURO Journal on Computational Optimization from Springer, EURO - The Association of European Operational Research Societies
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().