NDLI: Characterizing FJ and KKT Conditions in Nonconvex Mathematical Programming with Applications

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Mastroeni, Giandomenico Flores-Bazán, Fabián
Copyright Year	2015
Abstract	In this paper we analyze the Fritz John and Karush--Kuhn--Tucker (KKT) conditions for a (Gâteaux) differentiable nonconvex optimization problem with inequality constraints and a geometric constraint set. The Fritz John condition is characterized in terms of an alternative theorem which covers beyond standard situations, while characterizations of KKT conditions, without assuming constraints qualifications, are related to strong duality of a suitable linear approximation of the given problem and the properties of its associated image mapping. Such characterizations are suitable for dealing with some problems in structural optimization, where most of the known constraint qualifications fail. In particular, several examples are given showing the usefulness and optimality, in a certain sense, of our results, which provide much more information than those (including the Mordukhovich normal cone or Clarke's) appearing elsewhere. The case with a single inequality constraint is discussed in detail by establishing a hidden convexity in the validity of the KKT conditions. We outline possible applications to a class of mathematical programs with equilibrium constraints as well as to vector equilibrium or quasi-variational inequality problems.
Starting Page	647
Ending Page	676
Page Count	30
File Format	PDF
ISSN	10526234
DOI	10.1137/13094606X
e-ISSN	10957189
Journal	SIAM Journal on Optimization (SJOPE8)
Issue Number	1
Volume Number	25
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2015-03-19
Access Restriction	Subscribed
Subject Keyword	Optimality conditions, duality hidden convexity Applications of mathematical programming KKT conditions MPEC Nonconvex programming, global optimization FJ condition strong duality nonconvex optimization Sensitivity, stability, parametric optimization
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Software

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