A comparison of two approaches to second-order subdifferentiability concepts with application to optimality conditions

Eberhard, A and Pearce, C 2005, 'A comparison of two approaches to second-order subdifferentiability concepts with application to optimality conditions' in Liqun Qi, K. L. Teo, Xiaoqi Yang (ed.) Optimization and Control with Applications, Springer, New York, pp. 35-100.


Document type: Book Chapter
Collection: Book Chapters

Title A comparison of two approaches to second-order subdifferentiability concepts with application to optimality conditions
Author(s) Eberhard, A
Pearce, C
Year 2005
Title of book Optimization and Control with Applications
Publisher Springer
Place of publication New York
Editor(s) Liqun Qi, K. L. Teo, Xiaoqi Yang
Start page 35
End page 100
Subjects Optimisation
Applied Mathematics not elsewhere classified
Summary The graphical derivative and the coderivative when applied to the proximal subdifferential are in general not generated by a set of linear operators Nevertheless we find that in directions at which the subject (or subhessian) is supported, in a rank-1 sense, we have these supported operators interpolating the contingent cone. Thus under a prox-regularity assumption we are able to make a selection from the contingent graphical derivative in certain directions, using the exposed facets of a convex set of symmetric matrices. This allows us to make a comparison between some optimality conditions. A nonsmooth formulation of a standard smooth mathematical programming problem is used to derive a novel set of sufficient optimality conditions.
Copyright notice © Springer Science+Business Media., Inc
Keyword(s) optimization
nonsmooth analysis
subhessians
coderivative inclusions
rank-1 representers
optimality conditions
DOI - identifier 10.1007/0-387-24255-4_2
ISBN 0387242546
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