Algorithmic construction of the subdifferential from directional\n derivatives

2016/09/09 by Charles Audet, Audet, Charles, Warren Hare +1
Computer Science · Engineering · Mathematics · #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.1609.02928

openalex publication_date 2016/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The subdifferential of a function is a generalization for nonsmooth functions\nof the concept of gradient. It is frequently used in variational analysis,\nparticularly in the context of nonsmooth optimization. The present work\nproposes algorithms to reconstruct a polyhedral subdifferential of a function\nfrom the computation of finitely many directional derivatives. We provide upper\nbounds on the required number of directional derivatives when the space is\n R¹ and R², as well as in Rⁿ where subdifferential is known to\npossess at most three vertices.\n

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