A Fritz John Approach to First Order Optimality Conditions for Mathematical Programs with Equilibrium Constraints

Mathematical programs with equilibrium constraints (MPECs) are nonlinear programs which do not satisfy any of the common constraint qualifications. In order to obtain first order optimality conditions, constraint qualifications tailored to MPECs have been developed and researched in the past. This h...

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Bibliographic Details
Published inOptimization Vol. 52; no. 3; pp. 277 - 286
Main Authors Flegel, Michael L., Kanzow, Christian
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.06.2003
Subjects
Constraint Qualifications
First Order Conditions
Fritz John Conditions
Mathematical Programs With Equilibrium Constraints
Mathematics Subject Classification 2000: Primary: 90c46
Secondary: 90c30
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Summary:Mathematical programs with equilibrium constraints (MPECs) are nonlinear programs which do not satisfy any of the common constraint qualifications. In order to obtain first order optimality conditions, constraint qualifications tailored to MPECs have been developed and researched in the past. This has been done by falling back on technical proofs or results from nonsmooth analysis. In this article, we use a completely different approach and show how the standard Fritz John conditions may be used in order to obtain short and elementary proofs for the most important optimality conditions for MPECs. As a by-product, we obtain a new stationarity concept.
ISSN:0233-1934
1029-4945
DOI:10.1080/0233193031000120020