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Convergence Conditions for Nonlinear Programming Algorithms

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  • Willard I. Zangwill

    (The University of California, Berkeley)

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    Abstract

    Conditions which are necessary and sufficient for convergence of a nonlinear programming algorithm are stated. It is also shown that the convergence conditions can be easily applied to most programming algorithms. As examples, algorithms by Arrow, Hurwicz and Uzawa; Cauchy; Frank and Wolfe; and Newton-Raphson are proven to converge by direct application of the convergence conditions. Also the Topkis-Veinott convergence conditions for feasible direction algorithms are shown to be a special case of the conditions stated in this paper.

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    File URL: http://dx.doi.org/10.1287/mnsc.16.1.1
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 16 (1969)
    Issue (Month): 1 (September)
    Pages: 1-13

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    Handle: RePEc:inm:ormnsc:v:16:y:1969:i:1:p:1-13

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    Cited by:
    1. Pietersz, R. & Groenen, P.J.F., 2004. "Rank reduction of correlation matrices by majorization," Econometric Institute Research Papers EI 2004-11, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Jan Leeuw & Forrest Young & Yoshio Takane, 1976. "Additive structure in qualitative data: An alternating least squares method with optimal scaling features," Psychometrika, Springer, vol. 41(4), pages 471-503, December.
    3. Jochen Gorski & Frank Pfeuffer & Kathrin Klamroth, 2007. "Biconvex sets and optimization with biconvex functions: a survey and extensions," Computational Statistics, Springer, vol. 66(3), pages 373-407, December.

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