Optimum design in the presence of parametric uncertainty

  • B. M. Kwak
  • E. J. HaugJr.
Contributed Papers


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.

Key Words

Environmental parameter parametric optimal design first-order algorithm gradient projection with constraint error compensation min-max problem 


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  1. 1.
    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.Google Scholar
  2. 2.
    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.Google Scholar
  3. 3.
    McLinden, L.,Minimax Problems, Saddle Functions, and Duality, University of Wisconsin, Mathematics Research Center, MRC Technical Summary Report No. 1190, 1972.Google Scholar
  4. 4.
    Barry, P. E.,Optimal Control with Minimax Cost, State University of New York at Stony Brook, Electrical Sciences, PhD Thesis, 1969.Google Scholar
  5. 5.
    Danskin, J. M.,The Theory of Max-Min, Springer-Verlag, New York, New York, 1967.Google Scholar
  6. 6.
    Pshenichnyi, B. N.,Necessary Conditions for an Extremum (English translation), Marcel Dekker, New York, New York, 1971.Google Scholar
  7. 7.
    Heller, J. E.,A Gradient Algorithm for Minimax Design, University of Illinois, Coordinated Science Laboratory, Report No. R-406, 1969.Google Scholar
  8. 8.
    Medanic, J.,On Some Theoretical and Computational Aspects of the Minimax Problem, University of Illinois, Coordinated Science Laboratory, Report No. R-423, 1969.Google Scholar
  9. 9.
    Bracken, J., andMcGill, J. T.,Mathematical Programs with Optimization Problems in the Constraints, Operations Research, Vol. 21, No. 1, 1973.Google Scholar
  10. 10.
    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.Google Scholar
  11. 11.
    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.Google Scholar
  12. 12.
    Schmit, L. A.,et al.,Structural Synthesis, Vol. 1 Summer Course Notes, Case Institute of Technology, Cleveland, Ohio, 1965.Google Scholar
  13. 13.
    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.Google Scholar
  14. 14.
    Sved, G., andGinos, Z.,Structural Optimization under Multiple Loading, International Journal of Mechanical Sciences, Vol. 10, No. 10, 1968.Google Scholar
  15. 15.
    Fox, R. L.,Optimization Methods for Engineering Design, Addison-Wesley Publishing Company, Reading, Massachusetts, 1971.Google Scholar
  16. 16.
    Den Hartog, J. P.,Mechanical Vibrations, Second Edition, McGraw-Hill Book Company, New York, New York, 1940.Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • B. M. Kwak
    • 1
  • E. J. HaugJr.
    • 1
  1. 1.Department of Mechanics and Hydraulics, College of EngineeringThe University of IowaIowa City

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