Abstract
It is shown that a large class of engineering design problems are expressible as nonlinear semi-infinite programming problems. Methods for the solution of these SIP problems are surveyed.
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
Becker, R. G., A. J. Heunis, and D. Q. Mayne: Computer-Aided Design of Control Systems via Optimization”, Proc. IEE, vol. 126, no. 6, 1979.
Bhatti, M. A., T. Essebo, W. Nye, K. S. Pister, E. Polak, A. Sangiovanni Vincentelli, and A. Tits: “A Software System University of for Optimization Based Interactive Computer Aided Design”, Proc. IEEE I.S.C.A.S. Houston Tx., April 1980.
Bhatti, M.A., K. S. Pister, and E. Polak: “Optimal Design of an Earthquake Isolation System”, Proc. IUTAM Symp. on Structural Control, Univ. of Waterloo, Waterloo, Ont., Canada, June, 1979.
Bhatti, M.A., K. S. Pister, and E. Polak: “Optimization-Based, Interactive CAD of Dynamically Loaded structures”, to appear in Jour. of Structural Dynamics, of the A.S.C.E.
Bhatti, M. A., K. S. Pister, and E. Polak: “Optdyn — A General Purpose Optimization Program for Problems With or Without Dynamic Constraints”, Report No. UCB/EERC — 79/16, Earthquake Engineering Research Center, University of California, Berkeley, July 1979.
Brayton R.K., S.W. Director, and G.D. Hachtel: “Yield Maximization and Worst Case Design with Arbitrary Statistical Distributions”, IEEE Trans, on Circuits and Systems, Vol. CAS-27, n. 9, (1980).
Bandler, J. W., P. C. Liu, and H. Tromp: “Nonlinear Programming Approach to Optimal Design Centering Tolerancing and Tuning”, IEEE Trans. Vol. CAS-23, (1976).
Davison, E. J., and I. J. Ferguson: The Design of Controllers for the Multivariable Robust Servomechanism Problem Using Parameter Optimization Methods”, Systems Control Report No. 8002, University of Toronto, February 1980.
Gonzaga, C., and E. Polak: On Constraint Dropping Schemes and Optimality Functions for a Class of Outer Approximations Algorithms”, J. SIAM Control and Optimization Vol. 17, (1979).
Gonzaga, C., E. Polak and R. Trahan: “An Improved Algorithm for Optimization Problems with Functional Inequality Constraints”, IEEE Trans., Vol. AC-25, No. 1, (1980).
Hettich, R.: “Semi-Infinite Programming”, Springer-Verlag Lectlure Notes in Control and Information Sciences, Vol. 15, 1979.
Karmarkar J. S., and D. D. Siljak: “Maximization of Absolute Stability Regions by Mathematical Programming Methods”, Regelungtechnik No. 2, (1975).
Laub, A. J.: “An Inequality and Some Computations Related to the Robust Stability of Linear Dynamic Systems”, IEEE Trans, on Automatic Control Vol. AC-24, No. 2, (1979).
Mayne, D. Q., and E. Polak: “A Quadratically Convergent Algorithm for Solving Infinite-Dimensional Inequalities”, Memo No. UCB/ERL M80/11, University of California, Berkeley, 1980.
Mayne, D. Q., E. Polak and R. Trahan: “An Outer. Approximations Algorithm for Computer-Aided Design Problems”, JOTA, Vol. 28, No. 3, (1979).
Mayne, D. Q., E. Polak, and A. J. Heunis: “Solving Nonlinear Inequalities in a Finite Number of Iterations”, JOTA Vol. 33, No. 2, (1981).
Mayne, D. Q., E.Polak, and A. Voreadis: “A Cut Map Algorithm for Design Problems with Tolerances”, IEEE Trans. Vol. CAS-29, No. 1, (1982).
Mifflin, R.: “Semismooth and Semiconvex Functions in Constrained Optimization”, SIAM J. Control and Optimization, Vol. 15, No. 6, (1977).
Nye, W., E. Polak, A. Sangiovanni Vincentelli and A. Tits: “DELIGHT: an Optimization-Based Computer-Aided-Design System”, Proc. IEEE Int. Symp. on Circuits and Systems, Chicago, Ill, April 24–27, 1981.
Polak, E.: “Algorithms for a Class of Computer Aided Design Problems: A Review”, Automatica, Vol. 15, (1979).
Polak, E.: “An Implementable Algorithm for the Design Centering, Tolerancing and Tuning Problem”, JOTA, Vol. 35, No. 3, (1981).
Polak, E., and D. Q. Mayne: “An Algorithm for Optimization Problems with Functional Inequality Constraints”, IEEE Trans., Vol. AC-21, No. 2, (1976).
Polak, E., and D. Q. Mayne: “Algorithms for Computer Aided Design of Control Systems by the Method of Inequalities”, Proc. 18th IEE1 Conference on Decision and Control, Fort Lauderdale, Florida, Dec. 12–14, 1979.
Polak, E., and D. Q. Mayne: “Design of Nonlinear Feedback Controllers”, IEEE AC Trans. on Automatic Control, Vol AC-26, No. 3, (1981).
Polak, E., K. S. Pister, and D. Ray: “Optimal Design of Framed Structures Subjected to Earthquakes”, Eng. Optimization, Vol. 12, (1976).
Polak, E., and A. Sangiovanni Vincentelli: “Theoretical and Computational Aspects of the Optimal Design Centering, Tolerancing and Tuning Problem”, IEEE Trans. Vol CAS-26, No. 9, (1979).
Polak, E., and A. Tits: “A Recursive Quadratic Programming Algorithm for Semi-Infinite Optimization Problems”, University of California, Berkeley, ERL Memo No. UCB/ERL M80/50, 22 September, 1980.
Polak, E., and Y. Y. Wardi: “A Nondifferentiable Optimization Algorithm for the Design of Control Systems Subject to Singular Value Inequalities over a Frequency Range”, Proceedings IFAC/81 Congress, Kyoto, Japan, August 24–28, 1981.
Polak, E., R. Trahan, and D. Q. Mayne: “Combined Phase I — Phase II Methods of Feasible Directions”, Math. Programming, Vol. 17, No. 1, (1979).
Safonov, M. G., A. J. Laub, and G. L. Hartman: “Feedback Properties of Multivariable Systems: The Role and Use of the Return Difference Matrix”, IEEE Trans, on Control Vol. AC-26, (1981).
Sandel, N. R.: “Robust Stability of Systems with Applications to Singular Value Perturbations”, Automatica Vol. 15, (1979).
Taiwo, O.: “Design of a Multivariable Controller for a High Order Turbofan Engine Model by Zakian’s Method of Inequalities”, IEEE Trans. Vol. AC-23, No. 5, (1978).
Trahan, R., and E. Polak: “A Derivative Free Algorithm for a Class of Infinitely Constrained Optimization Problems”, IEEE Trans. Vol. AC-25, No. 1, (1979).
Zakian, V., and L. Al-Naib: “Design of Dynamical and Control Systems by the Method of Inequalities”, Proc. IEE, 120 (11), (1973).
Zakian, V.: “New Formulation for the Method of Inequalities”, Proc. IEE, 126(6), (1979).
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Polak, E. (1983). Semi-Infinite Optimization in Engineering Design. In: Fiacco, A.V., Kortanek, K.O. (eds) Semi-Infinite Programming and Applications. Lecture Notes in Economics and Mathematical Systems, vol 215. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46477-5_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-46477-5_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12304-0
Online ISBN: 978-3-642-46477-5
eBook Packages: Springer Book Archive