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

Abdelkrim El Mouatasim;  Rachid Ellaia;  Eduardo 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 Mouatasim;  Rachid Ellaia;  José 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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