2015/07/19 by Boris S. Mordukhovich, Mordukhovich, Boris S., M. Ebrahim Sarabi +1 · 1 citation
Computer Science · Engineering · Mathematics · #49J52 #49J53 #58C20 #Advanced Numerical Analysis Techniques #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1507.05347
openalex publication_date 2015/07/19 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
The paper is devoted to a comprehensive second-order study of a remarkable\nclass of convex extended-real-valued functions that is highly important in many\naspects of nonlinear and variational analysis, specifically those related to\noptimization and stability. This class consists of lower semicontinuous\nfunctions with possibly infinite values on finite-dimensional spaces, which are\nlabeled as piecewise linear ones and can be equivalently described via the\nconvexity of their epigraphs. In this the paper we calculate the second-order\nsubdifferentials (generalized Hessians) of arbitrary convex piecewise linear\nfunctions, together with the corresponding geometric objects, entirely in terms\nof their initial data. The obtained formulas allow us, in particular, to\njustify a new exact (equality-type) second-order sum rule for such functions in\nthe general nonsmooth setting.\n