PERTURBATIONS AND APPROXIMATE MINIMUM IN CONSTRAINED OPTIMIZATION

Abstract

An approximateminimum, for the minimization of a function f over a feasible set S, is a point » such that f (x) ¸ f (») ¡ ² for all feasible x near the minimum point p of f on S. This concept is relevant when the problem data, or the computation, are approximate. Under regularity assumptions, an approximate minimum is a local minimum of a perturbation of the given problem. This depends on the property of a strict local minimum, that a small perturbation moves the minimum point only by a small amount.