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A note on the optimization of constrained design problems

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Abstract

This paper describes a new algorithm for solving constrained optimization problems, based on a method proposed by Chattopadhyay. The proposed algorithm replaces the original problem withm constraints,m>1, by a sequence of optimization problems, with one constraint. Here, we modify the algorithm given by Chattopadhyay in order to make it applicable for a larger class of optimization problems and to improve its convergence characteristics.

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References

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    Chattopadhyay, R.,Optimization in Engineering Design, Journal of Optimization Theory and Applications, Vol. 9, No. 3, 1972.

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    Fiacco, A. V., andMcCormick, G. P.,The Sequential Unconstrained Minimization Technique for Non-linear Programming, a Primal-Dual Method, Management Sciences, Vol. 10, pp. 360–364, 1964.

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    Zangwill, W. I.,Non-linear Programming Via Penalty Functions, Management Sciences, Vol. 13, pp. 344–358, 1967.

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    Hestenes, M. R.,Multiplier and Gradient Methods, Journal of Optimization Theory and Applications, Vol. 4, No. 5, 1969.

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    Chattopadhyay, R.,A Study of Test Functions for Optimization Algorithms, Journal of Optimization Theory and Applications, Vol. 8, No. 3, 1971.

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Additional information

Partial support from the Graduate School of the University of Minnesota is gratefully acknowledged.

Communicated by D. G. Luenberger

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Stephanopoulos, G. A note on the optimization of constrained design problems. J Optim Theory Appl 17, 337–342 (1975). https://doi.org/10.1007/BF00933883

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Key Words

  • Bounds on cost functionals
  • engineering design
  • inequality constraints
  • mathematical programming
  • penalty-function methods