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The Sequential Unconstrained Minimization Technique for Nonlinear Programing, a Primal-Dual Method

Author

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  • Anthony V. Fiacco

    (Research Analysis Corporation, Bethesda, Maryland)

  • Garth P. McCormick

    (Research Analysis Corporation, Bethesda, Maryland)

Abstract

This article is based on an idea proposed by C. W. Carroll for transforming a mathematical programming problem into a sequence of unconstrained minimization problems. It describes the theoretical validation of Carroll's proposal for the convex programming problem. A number of important new results are derived that were not originally envisaged: The method generates primal-feasible and dual-feasible points, the primal objective is monotonically decreased, and a subproblem of the original programming problem is solved with each unconstrained minimization. Briefly surveyed is computational experience with a newly developed algorithm that makes the technique competitive with known methodology. (A subsequent article describing the computational algorithm is in preparation.)

Suggested Citation

  • Anthony V. Fiacco & Garth P. McCormick, 1964. "The Sequential Unconstrained Minimization Technique for Nonlinear Programing, a Primal-Dual Method," Management Science, INFORMS, vol. 10(2), pages 360-366, January.
    • Handle: RePEc:inm:ormnsc:v:10:y:1964:i:2:p:360-366
    DOI: 10.1287/mnsc.10.2.360
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    Cited by:

    1. Choi, Byung-Cheon & Park, Myoung-Ju, 2015. "A continuous time–cost tradeoff problem with multiple milestones and completely ordered jobs," European Journal of Operational Research, Elsevier, vol. 244(3), pages 748-752.

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