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Convergence Conditions for Nonlinear Programming Algorithms

Author

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  • Willard I. Zangwill

    (The University of California, Berkeley)

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.

Suggested Citation

  • Willard I. Zangwill, 1969. "Convergence Conditions for Nonlinear Programming Algorithms," Management Science, INFORMS, vol. 16(1), pages 1-13, September.
    • Handle: RePEc:inm:ormnsc:v:16:y:1969:i:1:p:1-13
    DOI: 10.1287/mnsc.16.1.1
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    Cited by:

    1. Raoul Pietersz & Patrick Groenen, 2004. "Rank reduction of correlation matrices by majorization," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 649-662.
    2. G Leonardi, 1978. "Optimum Facility Location by Accessibility Maximizing," Environment and Planning A, , vol. 10(11), pages 1287-1305, November.
    3. Jochen Gorski & Frank Pfeuffer & Kathrin Klamroth, 2007. "Biconvex sets and optimization with biconvex functions: a survey and extensions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 373-407, December.
    4. Ferrari, Paolo, 2005. "Road pricing and users' surplus," Transport Policy, Elsevier, vol. 12(6), pages 477-487, November.
    5. Sunil Dutta & Stefan J. Reichelstein, 2019. "Capacity Rights and Full Cost Transfer Pricing," CESifo Working Paper Series 7968, CESifo.
    6. Jan Leeuw & Forrest Young & Yoshio Takane, 1976. "Additive structure in qualitative data: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 41(4), pages 471-503, December.

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