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An SQP-Type Method and Its Application in Stochastic Programs

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  • Z. Wei

    (Guangxi University)

  • L. Qi

    (Hong Kong Polytechnic University)

  • X. Chen

    (Shimane University)

Abstract

In this paper, we propose and analyze an SQP-type method for solving linearly constrained convex minimization problems where the objective functions are too complex to be evaluated exactly. Some basic results for global convergence and local superlinear convergence are obtained according to the properties of the approximation sequence. We illustrate the applicability of our approach by proposing a new method for solving two-stage stochastic programs with fixed recourse.

Suggested Citation

  • Z. Wei & L. Qi & X. Chen, 2003. "An SQP-Type Method and Its Application in Stochastic Programs," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 205-228, January.
    • Handle: RePEc:spr:joptap:v:116:y:2003:i:1:d:10.1023_a:1022122521816
    DOI: 10.1023/A:1022122521816
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    References listed on IDEAS

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    1. Julia L. Higle & Suvrajeet Sen, 1992. "On the Convergence of Algorithms with Implications for Stochastic and Nondifferentiable Optimization," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 112-131, February.
    2. Liqun Qi & Houyuan Jiang, 1997. "Semismooth Karush-Kuhn-Tucker Equations and Convergence Analysis of Newton and Quasi-Newton Methods for Solving these Equations," Mathematics of Operations Research, INFORMS, vol. 22(2), pages 301-325, May.
    3. Julia L. Higle & Suvrajeet Sen, 1991. "Stochastic Decomposition: An Algorithm for Two-Stage Linear Programs with Recourse," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 650-669, August.
    4. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
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    Cited by:

    1. Gonglin Yuan & Xiaoliang Wang & Zhou Sheng, 2020. "The Projection Technique for Two Open Problems of Unconstrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 590-619, August.

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