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Second-Order Analysis of Piecewise Linear Functions with Applications to Optimization and Stability

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Abstract

This paper is devoted to second-order variational analysis of a rather broad class of extended-real-valued piecewise liner functions and their applications to various issues of optimization and stability. Based on our recent explicit calculations of the second-order subdifferential for such functions, we establish relationships between nondegeneracy and second-order qualification for fully amenable compositions involving piecewise linear functions. We then provide a second-order characterization of full stable local minimizers in composite optimization and constrained minimax problems.

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Acknowledgments

The authors are grateful to the referees for their helpful remarks. This research was partly supported by the National Science Foundation under grants DMS-1007132 and DMS-1512846 and by the Air Force Office of Scientific Research Grant #15RT0462.

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Authors and Affiliations

  1. Wayne State University, Detroit, MI, USA

    B. S. Mordukhovich & M. E. Sarabi

Authors
  1. B. S. Mordukhovich
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  2. M. E. Sarabi
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Correspondence to M. E. Sarabi.

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Communicated by Aram Arutyunov.

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Mordukhovich, B.S., Sarabi, M.E. Second-Order Analysis of Piecewise Linear Functions with Applications to Optimization and Stability. J Optim Theory Appl 171, 504–526 (2016). https://doi.org/10.1007/s10957-016-0897-y

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  • DOI: https://doi.org/10.1007/s10957-016-0897-y

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