Variational Analysis

Wim Stefanus Ackooij and Welington Luis Oliveira
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Wim Stefanus Ackooij: Électricité de France (EDF R&D)
Welington Luis Oliveira: Mines Paris - PSL

Chapter Chapter 3 in Methods of Nonsmooth Optimization in Stochastic Programming, 2025, pp 61-94 from Springer

Abstract: Abstract In this chapter, we will discuss tools from variational analysis that will be useful when analysing the convergence of algorithms. Our main focus will be on locally Lipschitzian functions, for which generalized directional derivatives and subdifferential can be defined. For the latter, our focus will mostly be on Clarke’s subdifferential, but other possibilities exist also. We will briefly mention these as well. The chapter also covers the topic of constraint qualification, in other words, conditions allowing us to express the geometry of a given set of constraints in optimality conditions, in terms of nominal underlying data.

Keywords: Non-convex geometry; Subdifferentiability; Optimality conditions; Variational analysis (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-3-031-84837-7_3

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DOI: 10.1007/978-3-031-84837-7_3

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