J Austral Math Soc Ser B 36 pp50--59, 1994.

Convergence of discrete approximations for constrained minimization

B. D. Craven

Abstract

If a constrained minimization problem, under Lipschitz or uniformly continuous hypotheses on the functions, has a strict local minimum, then a small perturbation of the functions leads to a minimum of the perturbed problem, close to the unperturbed minimum. Conditions are given for the perturbed minimum point to be a Lipschitz function of a perturbation parameter. This is used to study convergence rate for a problem of continuous programming, when the variable is approximated by step-functions. Similar conclusions apply to computation of optimal control problems, approximating the control function by step-functions.

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Author

B. D. Craven

Mathematics Department, University of Melbourne, Parkville, Victoria 3052, Australia.