A Modified Relaxation Scheme for Mathematical Programs with Complementarity Constraints

Gui-Hua Lin () and Masao Fukushima ()

Annals of Operations Research, 2005, vol. 133, issue 1, 63-84

Abstract: In this paper, we consider a mathematical program with complementarity constraints. We present a modified relaxed program for this problem, which involves less constraints than the relaxation scheme studied by Scholtes (2000). We show that the linear independence constraint qualification holds for the new relaxed problem under some mild conditions. We also consider a limiting behavior of the relaxed problem. We prove that any accumulation point of stationary points of the relaxed problems is C-stationary to the original problem under the MPEC linear independence constraint qualification and, if the Hessian matrices of the Lagrangian functions of the relaxed problems are uniformly bounded below on the corresponding tangent space, it is M-stationary. We also obtain some sufficient conditions of B-stationarity for a feasible point of the original problem. In particular, some conditions described by the eigenvalues of the Hessian matrices mentioned above are new and can be verified easily. Copyright Springer Science + Business Media, Inc. 2005

Keywords: mathematical program with complementarity constraints; (MPEC-)linear independence constraint qualification; nondegeneracy; (B-; M-; C-)stationarity; weak second-order necessary conditions; upper level strict complementarity (search for similar items in EconPapers)
Date: 2005
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (20)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10479-004-5024-z (text/html)
Access to full text is restricted to subscribers.

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:annopr:v:133:y:2005:i:1:p:63-84:10.1007/s10479-004-5024-z

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-004-5024-z

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().