Methods for optimal engineering design problems based on globally convergent methods

Abstract

An optimal design problem is formulated as a system of nonlinear equations rather than the extremum of a functional. Based on the Chow-Yorke algorithm, another globally convergent homotopy method, and quasi-Newton methods, two algorithms are developed for solving the nonlinear system. Although the base algorithms are globally convergent (under certain fairly general assumptions), there is no theoretical proof of global convergence for the new methods. Some low dimensional numerical results are given.