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A Comparison of Two Approaches to Second-Order Subdifferentiability Concepts with Application to Optimality Conditions

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Optimization and Control with Applications

Part of the book series: Applied Optimization ((APOP,volume 96))

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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Authors and Affiliations

  1. Department of Mathematics, RMIT University, GPO Box 2476V, Melbourne, Australia

    A. Eberhard

  2. Department of Mathematics, University of Adelaide, North Terrace, Adelaide, Australia

    C. E. M. Pearce

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  1. A. Eberhard
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  2. C. E. M. Pearce
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Editors and Affiliations

  1. The Hong Kong Polytechnic University, Hong Kong

    Liqun Qi , Koklay Teo  & Xiaoqi Yang ,  & 

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Eberhard, A., Pearce, C.E.M. (2005). A Comparison of Two Approaches to Second-Order Subdifferentiability Concepts with Application to Optimality Conditions. In: Qi, L., Teo, K., Yang, X. (eds) Optimization and Control with Applications. Applied Optimization, vol 96. Springer, Boston, MA. https://doi.org/10.1007/0-387-24255-4_2

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