Solving Mathematical Programs with Equilibrium Constraints

Lei Guo (), Gui-Hua Lin () and Jane J. Ye ()
Additional contact information
Lei Guo: Shanghai Jiao Tong University
Gui-Hua Lin: Shanghai University
Jane J. Ye: University of Victoria

Journal of Optimization Theory and Applications, 2015, vol. 166, issue 1, No 11, 234-256

Abstract: Abstract This paper aims at developing effective numerical methods for solving mathematical programs with equilibrium constraints. Due to the existence of complementarity constraints, the usual constraint qualifications do not hold at any feasible point, and there are various stationarity concepts such as Clarke, Mordukhovich, and strong stationarities that are specially defined for mathematical programs with equilibrium constraints. However, since these stationarity systems contain some unknown index sets, there has been no numerical method for solving them directly. In this paper, we remove the unknown index sets from these stationarity systems successfully, and reformulate them as smooth equations with box constraints. We further present a modified Levenberg–Marquardt method for solving these constrained equations. We show that, under some weak local error bound conditions, the method is locally and superlinearly convergent. Furthermore, we give some sufficient conditions for local error bounds, and show that these conditions are not very stringent by a number of examples.

Keywords: Mathematical program with equilibrium constraints; Clarke/Mordukhovich/strong stationarity; Levenberg–Marquardt method; Error bound; 90C26; 90C30; 90C33 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (15)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-014-0699-z 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:166:y:2015:i:1:d:10.1007_s10957-014-0699-z

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

DOI: 10.1007/s10957-014-0699-z

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 ().