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A new approach to constrained function optimization

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Abstract

A new approach to the constrained function optimization problem is presented. It is shown that the ordinary Lagrange multiplier method and the penalty function method may be generalized and combined, and the new concept ofmultiplier function is introduced. The problem may then be converted into an unconstrained well-conditioned optimization problem. Methods for numerical solution are discussed, and new algorithms are derived.

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References

  1. Fiacco, A. V., andMcCormick, G. P.,Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John Wiley and Sons, New York, New York, 1968.

    MATH  Google Scholar 

  2. Powell, M. J. D.,A Method for Nonlinear Constraints in Minimization Problems, Optimization, Edited by R. Fletcher, Academic Press, London, England, 1969.

    Google Scholar 

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

  4. Mårtensson, K.,Methods for Constrained Function Minimization, Lund Institute of Technology, Division of Automatic Control, Research Report No. 7101, 1971.

  5. Fletcher, R.,Methods for Nonlinear Programming, Integer and Nonlinear Programming, Edited by J. Abadie, North-Holland Publishing Company, Amsterdam, Holland, 1970.

    Google Scholar 

  6. Mangasarian, O. L.,Nonlinear Programming, McGraw-Hill Book Company, New York, New York, 1968.

    Google Scholar 

  7. Gantmacher, F. R.,The Theory of Matrices, Vol. 1, Chelsea Publishing Company, New York, New York, 1960.

    Google Scholar 

  8. Powell, M. J. D.,An Efficient Method for Finding the Minimum of a Function of Several Variables without Calculating Derivatives, Computer Journal, Vol. 7, No. 4, 1964.

  9. Stewart, G. W., III,A Modification of Davidon's Minimization Method to Accept Difference Approximations of Derivatives, Journal of the Association for Computing Machinery, Vol. 14, No. 1, 1967.

  10. Davidon, W. C.,Variable Metric Method for Minimization, Argonne National Laboratory, Report No. ANL-5990, 1959.

  11. Fletcher, R., andPowell, M. J. D.,A Rapidly Convergent Descent Method for Minimization, Computer Journal, Vol. 6, No. 2, 1963.

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Authors and Affiliations

  1. Division of Automatic Control, Lund Institute of Technology, Lund, Sweden

    K. Mårtensson (Research Associate)

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  1. K. Mårtensson
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Communicated by M. R. Hestenes

The author wishes to express his gratitude to Professor K. J. Åström for his encouragement and assistance and to Professor P. Falb for valuable suggested improvements. This work was supported by the Swedish Board for Technical Development, Contract No. 70-337/U270.

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Mårtensson, K. A new approach to constrained function optimization. J Optim Theory Appl 12, 531–554 (1973). https://doi.org/10.1007/BF00934776

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  • DOI: https://doi.org/10.1007/BF00934776

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