A Homotopy Approach for Solving Constrained Optimization Problems

Abstract

A homotopy approach for solving constrained parameter optimization problems is examined. The first order necessary conditions, with the complementavity conditions represented using a technique due to Mangasarian, are solved. The equations are augmented to avoid singularities which occur when the active constraint changes. The Chow -Torke algorithm is used to track the homotopy path leading to the solution to the desired problem at the terminal point. A simple example which illustrates the technique, and an application to a fuel optimal orbital transfer problem are presented.