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Variational Analysis

In: Methods of Nonsmooth Optimization in Stochastic Programming

Author

Listed:
  • Wim Stefanus Ackooij

    (Électricité de France (EDF R&D))

  • Welington Luis Oliveira

    (Mines Paris - PSL)

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.

Suggested Citation

  • Wim Stefanus Ackooij & Welington Luis Oliveira, 2025. "Variational Analysis," International Series in Operations Research & Management Science, in: Methods of Nonsmooth Optimization in Stochastic Programming, chapter 0, pages 61-94, Springer.
    • Handle: RePEc:spr:isochp:978-3-031-84837-7_3
    DOI: 10.1007/978-3-031-84837-7_3
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