A Homotopy Approach for Solving Constrained Optimization Problems

A homotopy approach for solving constrained parameter optimization problems is examined. The first order necessary conditions with the conditions on the inequality constraints, 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-Yorke algorithm is used to track the solutions to the modified set which result in the solution to the desired problem at the terminal point. A simple example is presented which illustrates the technique and applications to a few fuel optimal orbital transfer problems are presented.