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A note on strong pseudoconvexity

100%
Ivanov V.
Open Mathematics
|
2008
|
tom 6
|
nr 4
576-580
EN
A strongly pseudoconvex function is generalized to non-smooth settings. A complete characterization of the strongly pseudoconvex radially lower semicontinuous functions is obtained.
2
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Random perturbation of the variable metric method for unconstrained nonsmooth nonconvex optimization

100%
Mouatasim A. E., Ellaia R., Souza De Cursi J. E.
International Journal of Applied Mathematics and Computer Science
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2006
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tom 16
|
nr 4
463-474
EN
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.
3
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Random perturbation of the projected variable metric method for nonsmooth nonconvex optimization problems with linear constraints

100%
El Mouatasim A., Ellaia R., Souza de Cursi E.
International Journal of Applied Mathematics and Computer Science
|
2011
|
tom 21
|
nr 2
317-329
EN
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.
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