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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.

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