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Random perturbation of the variable metric method for unconstrained nonsmooth nonconvex optimization. (English) Zbl 1160.90694

Summary: We consider the global optimization of a nonsmooth (nondifferentiable) nonconvex real function. We introduce a variable metric descent method adapted to nonsmooth situations, which is modified by the incorporation of suitable random perturbations. Convergence to a global minimum is established and a simple method for the generation of suitable perturbations is introduced. An algorithm is proposed and numerical results are presented, showing that the method is computationally effective and stable.

MSC:

90C55 Methods of successive quadratic programming type
90C30 Nonlinear programming
49J52 Nonsmooth analysis

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