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Model-Based Methods in Derivative-Free Nonsmooth Optimization

In: Numerical Nonsmooth Optimization

Author

Listed:
  • Charles Audet

    (École Polytechnique de Montréal, GERAD and Département de Mathématiques et Génie Industriel)

  • Warren Hare

    (University of British Columbia, Department of Mathematics)

Abstract

Derivative-free optimization (DFO) is the mathematical study of the optimization algorithms that do not use derivatives. One branch of DFO focuses on model-based DFO methods, where an approximation of the objective function is used to guide the optimization algorithm. Historically, model-based DFO has often assumed that the objective function is smooth, but unavailable analytically. However, recent progress has brought model-based DFO into the realm of nonsmooth optimization (NSO). In this chapter, we survey some of the progress of model-based DFO for nonsmooth functions. We begin with some historical context on model-based DFO. From there, we discuss methods for constructing models of smooth functions and their accuracy. This leads to modelling techniques for nonsmooth functions and a discussion on several frameworks for model-based DFO for NSO. We conclude the chapter with some of our opinions on profitable research directions in model-based DFO for NSO.

Suggested Citation

  • Charles Audet & Warren Hare, 2020. "Model-Based Methods in Derivative-Free Nonsmooth Optimization," Springer Books, in: Adil M. Bagirov & Manlio Gaudioso & Napsu Karmitsa & Marko M. Mäkelä & Sona Taheri (ed.), Numerical Nonsmooth Optimization, chapter 0, pages 655-691, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-34910-3_19
    DOI: 10.1007/978-3-030-34910-3_19
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