CONVERGENCE OF DISCRETE APPROXIMATIONS FOR CONSTRAINED MINIMIZATION

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