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Optimization of upper semidifferentiable functions. (English) Zbl 0534.90069
In this paper, we present an implementable algorithm to minimize a nonconvex, nondifferentiable function in \({\mathbb{R}}^ m\). 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 a special case, the enlargement proposed by Goldstein. We analyze the convergence of the method and discuss some numerical experiments.

90C30 Nonlinear programming
49M37 Numerical methods based on nonlinear programming
65K05 Numerical mathematical programming methods
26B05 Continuity and differentiation questions
Full Text: DOI
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