A sub-additive DC approach to the complementarity problem

L. Abdallah (), M. Haddou () and T. Migot ()
Additional contact information
L. Abdallah: Lebanese University
M. Haddou: Univ Rennes
T. Migot: University of Guelph

Computational Optimization and Applications, 2019, vol. 73, issue 2, No 6, 509-534

Abstract: Abstract In this article, we study a merit function based on sub-additive functions for solving the non-linear complementarity problem (NCP). This leads to consider an optimization problem that is equivalent to the NCP. In the case of a concave NCP this optimization problem is a Difference of Convex (DC) program and we can therefore use DC Algorithm to locally solve it. We prove that in the case of a concave monotone NCP, it is sufficient to compute a stationary point of the optimization problem to obtain a solution of the complementarity problem. In the case of a general NCP, assuming that a DC decomposition of the complementarity problem is known, we propose a penalization technique to reformulate the optimization problem as a DC program and prove that local minima of this penalized problem are also local minima of the merit problem. Numerical results on linear complementarity problems, absolute value equations and non-linear complementarity problems show that our method is promising.

Keywords: Complementarity problem; Difference of convex; Merit function; DC algorithm; 90C59; 90C30; 90C33; 65K05; 49M20 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-019-00078-w 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:coopap:v:73:y:2019:i:2:d:10.1007_s10589-019-00078-w

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-019-00078-w

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

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