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

Date

2005

Authors

Eberhard, A.
Pearce, C.

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Qi, L.
Teo, K.
Yang, X.

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Book chapter

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Applied optimization - Optimization and control with applications, 2005 / Qi, L., Teo, K., Yang, X. (ed./s), pp.35-100

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Abstract

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.

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The original publication is available at www.springerlink.com

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