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

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.