Abstract
In this paper, we present an implementable algorithm to minimize a nonconvex, nondifferentiable function in ℝm. The method generalizes Wolfe's algorithm for convex functions and Mifflin's algorithm for semismooth functions to a broader class of functions, so-called upper semidifferentiable. With this objective, we define a new enlargement of Clarke's generalized gradient that recovers, in special cases, the enlargement proposed by Goldstein. We analyze the convergence of the method and discuss some numerical experiments.
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Communicated by D. Q. Mayne
The author would like to thank J. B. Hiriart-Urruty (Toulouse) for having provided him with Definition 2.1 and the referees for their constructive remarks about a first version of the paper.
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Bihain, A. Optimization of upper semidifferentiable functions. J Optim Theory Appl 44, 545–568 (1984). https://doi.org/10.1007/BF00938396
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DOI: https://doi.org/10.1007/BF00938396