Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Y. Sawaragi, H. Nakayama, and T. Tanino, Theory of Multiobjective Optimization, Academic Press (1985).
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).
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).
W.T. Nye, DELIGHT: An Interactive System for Optimization-Based Engineering Design, Ph.D. Thesis, Department EECS, University of California, Berkeley, California (1983).
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).
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).
S.P. Han, “Superlinear Convergence of a Minirnax Method,” TR78–336, Department of Computer Science, Cornell University (1978).
S.P. Han, “Variable Metric Methods for Minimizing a Class of Nondifferentiable Functions.- Math. Prog. vol. 20, pp. 1–13 (1981).
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).
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).
D. Q. Mayne and E. Polak, “A Superlinearly Convergent Algorithm for Constrained Optimiza-tion Problems,” Mathematical Programniing Study vol. 16, pp. 45–61 (1982).
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).
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).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Panier, E.R., Tits, A.L. (1986). A Superlinearly Convergent Method of Feasible Directions for Optimization Problems Arising in the Design of Engineering Systems. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007547
Download citation
DOI: https://doi.org/10.1007/BFb0007547
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16729-7
Online ISBN: 978-3-540-39856-1
eBook Packages: Springer Book Archive