Abstract
A new class of optimal design problems that incorporates environmental uncertainty is formulated and related to worst-case design, minimax objective design, and game theory. A numerical solution technique is developed and applied to a weapon allocation problem, a structural design problem with an infinite family of load conditions, and a vibration isolator design problem with a band of excitation frequencies.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
John, F.,Extremum Problems with Inequalities as Subsidiary Conditions, Studies and Essays, Courant Anniversary Volume, Edited by K. O. Friedricks, O. E. Neugebauer, and J. J. Stokes, John Wiley and Sons (Interscience Publishers), New York, New York, 1948.
Gehner, K. R.,Necessary and Sufficient Optimality Conditions for the Fritz John Problem with Linear Equality Constraints, SIAM Journal on Control, Vol. 12, No. 1, 1974.
McLinden, L.,Minimax Problems, Saddle Functions, and Duality, University of Wisconsin, Mathematics Research Center, MRC Technical Summary Report No. 1190, 1972.
Barry, P. E.,Optimal Control with Minimax Cost, State University of New York at Stony Brook, Electrical Sciences, PhD Thesis, 1969.
Danskin, J. M.,The Theory of Max-Min, Springer-Verlag, New York, New York, 1967.
Pshenichnyi, B. N.,Necessary Conditions for an Extremum (English translation), Marcel Dekker, New York, New York, 1971.
Heller, J. E.,A Gradient Algorithm for Minimax Design, University of Illinois, Coordinated Science Laboratory, Report No. R-406, 1969.
Medanic, J.,On Some Theoretical and Computational Aspects of the Minimax Problem, University of Illinois, Coordinated Science Laboratory, Report No. R-423, 1969.
Bracken, J., andMcGill, J. T.,Mathematical Programs with Optimization Problems in the Constraints, Operations Research, Vol. 21, No. 1, 1973.
Bracken, J., andMcGill, J. T.,Computer Program for Solving Mathematical Programs with Nonlinear Programs in the Constraints, Institute for Defense Analyses, Program Analysis Division, Paper No. P-801, 1972.
Haug, E. J., Jr.,Engineering Design Handbook, Computer Aided Design of Mechanical Systems, AMCP 706-192, U.S. Army Materiel Command, Washington, D.C., 1973.
Schmit, L. A.,et al.,Structural Synthesis, Vol. 1 Summer Course Notes, Case Institute of Technology, Cleveland, Ohio, 1965.
Haug, E. J., Jr., andArora, J. S.,Structural Optimization via Steepest Descent and Interactive Computation, Proceedings of the Third Conference on Matrix Methods in Structural Mechanics, Wright-Patterson AFB, Ohio, 1971.
Sved, G., andGinos, Z.,Structural Optimization under Multiple Loading, International Journal of Mechanical Sciences, Vol. 10, No. 10, 1968.
Fox, R. L.,Optimization Methods for Engineering Design, Addison-Wesley Publishing Company, Reading, Massachusetts, 1971.
Den Hartog, J. P.,Mechanical Vibrations, Second Edition, McGraw-Hill Book Company, New York, New York, 1940.
Author information
Authors and Affiliations
Additional information
Communicated by C. T. Leondes
Rights and permissions
About this article
Cite this article
Kwak, B.M., Haug, E.J. Optimum design in the presence of parametric uncertainty. J Optim Theory Appl 19, 527–546 (1976). https://doi.org/10.1007/BF00934653
Issue Date:
DOI: https://doi.org/10.1007/BF00934653