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

Author

Listed:
  • B. S. Mordukhovich

    (Wayne State University)

  • M. E. Sarabi

    (Wayne State University)

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.

Suggested Citation

  • B. S. Mordukhovich & M. E. Sarabi, 2016. "Second-Order Analysis of Piecewise Linear Functions with Applications to Optimization and Stability," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 504-526, November.
    • Handle: RePEc:spr:joptap:v:171:y:2016:i:2:d:10.1007_s10957-016-0897-y
    DOI: 10.1007/s10957-016-0897-y
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    References listed on IDEAS

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    1. B. S. Mordukhovich & T. T. A. Nghia & R. T. Rockafellar, 2015. "Full Stability in Finite-Dimensional Optimization," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 226-252, February.
    2. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
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