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

B. S. Mordukhovich () and M. E. Sarabi ()
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B. S. Mordukhovich: Wayne State University
M. E. Sarabi: Wayne State University

Journal of Optimization Theory and Applications, 2016, vol. 171, issue 2, No 10, 504-526

Abstract: 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.

Keywords: Variational analysis and optimization; Piecewise linear functions; Second-order subdifferentials; Nondegeneracy; Full stability of local minimizers; 49J52; 90C30; 90C31 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-016-0897-y

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