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Optimization problems with convex epigraphs. Application to optimal control

100%

Kryazhimskii A. V.

International Journal of Applied Mathematics and Computer Science

2001

tom 11

nr 4

773-801

For a class of infinite-dimensional minimization problems with nonlinear equality constraints, an iterative algorithm for finding global solutions is suggested. A key assumption is the convexity of the ''epigraph'', a set in the product of the image spaces of the constraint and objective functions. A convexification method involving randomization is used. The algorithm is based on the extremal shift control principle due to N.N. Krasovskii. An application to a problem of optimal control for a bilinear control system is described.

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

70%

Mouatasim A. E., Ellaia R., Souza De Cursi J. E.

International Journal of Applied Mathematics and Computer Science

2006

tom 16

nr 4

463-474

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.

Ograniczanie wyników

2 International Journal of Applied Mathematics and Computer Science

1 Ellaia R.

1 Kryazhimskii A. V.

1 Mouatasim A. E.

1 Souza De Cursi J. E.

1 2006

1 2001

Wyniki wyszukiwania

Optimization problems with convex epigraphs. Application to optimal control

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