Homotopy Curve Tracking in Approximate Interior Point Optimization
نویسندگان
چکیده
The use of computer simulations has revolutionized the way engineers design and improve products and affects all design stages from concept to realization. As a consequence optimization has become an important tool for the engineer to realize better designs without the need of extensive prototype building. One of the algorithms that has shown an important ability to deal with this type of optimization is known as sequential approximate optimization. In sequential approximate optimization a series of local minimizations are performed over local response surface approximations of the system. In a previous work the authors developed an interior point approach for trust region managed sequential approximate optimization. The interior point approach insures that approximate feasibility is maintained throughout the optimization process. In the case of an infeasible design point, a relaxation of the constraints allows the algorithm to operate without modification. The relaxation is controlled by and homotopy parameter. A primary advantage resides in the fact that all the constraints influence the optimization, since the relaxation fades at the same time for all violated constraints. Adjustment of the parameter was performed in an heuristic fashion. In this paper the authors present a robust methodology to update the homotopy parameter based on the theory of probability one homotopies for nonlinear programming. Results show that the method is robust and effective in its imple∗Graduate Research Assistant, Student Member AIAA †Professor, Associate Fellow AIAA ‡Professor. Copyright 2003 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. mentation.
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