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Random perturbation of the projected variable metric method for nonsmooth nonconvex optimization problems with linear constraints

Abdelkrim El MouatasimRachid EllaiaEduardo Souza de Cursi — 2011

International Journal of Applied Mathematics and Computer Science

We present a random perturbation of the projected variable metric method for solving linearly constrained nonsmooth (i.e., nondifferentiable) nonconvex optimization problems, and we establish the convergence to a global minimum for a locally Lipschitz continuous objective function which may be nondifferentiable on a countable set of points. Numerical results show the effectiveness of the proposed approach.

Random perturbation of the variable metric method for unconstrained nonsmooth nonconvex optimization

Abdelkrim El MouatasimRachid EllaiaJosé Souza de Cursi — 2006

International Journal of Applied Mathematics and Computer Science

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....

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