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Second-order analysis of piecewise linear functions with applications to optimization and stability

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arxiv 1507.05350 v2 pith:ZNOF4VTB submitted 2015-07-19 math.OC

Boris S. Mordukhovich , M. Ebrahim Sarabi This is my paper · ORCID
classification math.OC
keywords second-orderfunctionsoptimizationpiecewiseanalysisapplicationslinearstability
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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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