A Globally Convergent Algorithm with Adaptively Refined Discretization for Semi-Infinite Optimization Problems Arising in Engineering Design.

Abstract

Optimization problems arising in engineering design often exhibit specific features which, in the interest of computational efficiency, ought to be exploited. Such is the possible presence of 'functional' specifications, i.e., specifications that are to be met over an interval of values of an independent parameter such as time or frequency. Such problems pertain to semiinfinite optimization. While most of the algorithms that have been proposed for the solution of these problems make use, at each iteration, of a set of local maximizers over the range of the independent parameter, the question of suitably approximating such maximizers is generally left aside. It has been suggested that this issue can be addressed by means of an adaptively refined discretization of the interval of variation of the independent parameter. The algorithm proposed in this paper makes use of such a technique and, by means of a certain memory mechanism, avoids the potential lack of convergence suffered by an existing algorithm.