Adaptive Global Algorithm for Solving Box-Constrained Non-convex Quadratic Minimization Problems

Amar Andjouh and Mohand Ouamer Bibi
Additional contact information
Amar Andjouh: Faculty of the Exact Sciences, University of Bejaia
Mohand Ouamer Bibi: Faculty of the Exact Sciences, University of Bejaia

Journal of Optimization Theory and Applications, 2022, vol. 192, issue 1, No 15, 360-378

Abstract: Abstract In this paper, we propose a new adaptive method for solving the non-convex quadratic minimization problem subject to box constraints, where the associated matrix is indefinite, in particular with one negative eigenvalue. We investigate the derived sufficient global optimality conditions by exploiting the particular form of the Moreau envelope (L-subdifferential) of the quadratic function and abstract convexity, also to develop a new algorithm for solving the original problem without transforming it, that we call adaptive global algorithm, which can effectively find one global minimizer of the problem. Furthermore, the research of the convex support of the objective function allows us to characterize the global optimum and reduce the complexity of the big size problems. We give some theoretical aspects of global optimization and present numerical examples with test problems for illustrating our approach.

Keywords: Global optimization; Non-convex quadratic minimization; Optimality conditions; Box constraints; Convex support; Abstract convexity; Adaptive global algorithm (AGA) (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-021-01980-2 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:joptap:v:192:y:2022:i:1:d:10.1007_s10957-021-01980-2

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-021-01980-2

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().