A Superlinearly Convergent Method of Feasible Directions for Optimization Problems Arising in the Design of Engineering Systems
Engineering design problems often involve the solution of one or several constrained minimax optimization problems. It is sometimes crucial that all iterates constructed when solving such problems satisfy a given set of ‘hard’ inequality constraints, and generally desirable that the (maximum) objective function value improve at each iteration. In this paper, we propose an algorithm of the sequential quadratic programming (SQP) type that enjoys such properties. This algorithm is inspired from an algorithm recently proposed for the solution of single objective constrained optimization problems. Preliminary numerical results are promising.
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- Y. Sawaragi, H. Nakayama, and T. Tanino, Theory of Multiobjective Optimization, Academic Press (1985).Google Scholar
- W.T. Nye and A.L. Tits, “An Application-Oriented, Optimization-Based Methodology for Interac-tive Design of Engineering Systems,” International Journal of Control vol. 43, no. 6, pp. 1693–1721 (1986).Google Scholar
- Z. Ma and A.L. Tits, “Interaction, Specification Refinement, and Tradeoff Exploration in Optimization-Ba,sed Design of Engineering Systems,” Proceedings of the 1985 IFAC Workshop on Control Applications of Nonlinear Programming and Optiinization, pp. 180–194 Pergamon Press, (1986).Google Scholar
- W.T. Nye, DELIGHT: An Interactive System for Optimization-Based Engineering Design, Ph.D. Thesis, Department EECS, University of California, Berkeley, California (1983).Google Scholar
- M.K.H. Fan, C.D. Walrath, C. Lee, A.L. Tits, W.T. Nye, M. Rimer, R.T. Grant, and W.S. Levine. “Two Case Studies in Optimization-Based Computer-Aided Design of Control Systems,” Proceed-ings of the 24th IEEE Conf. on Decision and Control, p. 1794 (December 1985).Google Scholar
- W.T. Nye, A.Sangiovanni-Vincentelli, J.P. Spoto, and A.L. Tits, “DELIGHT.SPICE: An Optimization-Based System for the Design of Integrated Circuits,” Proceedings of the 1988 Cus-tom Integrated Circuits Conference, pp. 233–238 (May 1983).Google Scholar
- S.P. Han, “Superlinear Convergence of a Minirnax Method,” TR78–336, Department of Computer Science, Cornell University (1978).Google Scholar
- E.R. Panier and A.L. Tits, “A Superlinearly Convergent Feasible Method for the Solution of Ine-quality Constrained Optimization Problems,” SIAM J. on Control and Optimization (1986. to appear).Google Scholar
- M.J.D. Powell, “A Fast Algorithm for Nonlinearly Constrained Optimization Calculations,” pp. 144–157 in Numerical Analysis, Dundee, 1977, Lecture Notes in Mathematics 630, ed. G.A. Wat-son, Springer-Verlag (1977).Google Scholar
- N. Maratos, Exact Penalty Function Algorithms for Finite Dimensional and Optim _ation Prob-lems, Ph.D. Thesis, Imperial College of Science and Technology, London, U.K. (1978).Google Scholar
- W.T. Nye, E. Polak, A. Sangiovanni-Vincentelli, and A. L. Tits, “DELIGHT: An Optimization-Based Computer-Aided Design System,” Proceedings of the 1981 IEEE International Symposium on Circuits and Systems, pp. 851–855 (April 1981).Google Scholar