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Minimization Algorithms Based on Supervisor and Searcher Cooperation

Author

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  • W. Liu

    (University of Kent)

  • Y. H. Dai

    (Chinese Academy of Sciences)

Abstract

In the present work, we explore a general framework for the design of new minimization algorithms with desirable characteristics, namely, supervisor-searcher cooperation. We propose a class of algorithms within this framework and examine a gradient algorithm in the class. Global convergence is established for the deterministic case in the absence of noise and the convergence rate is studied. Both theoretical analysis and numerical tests show that the algorithm is efficient for the deterministic case. Furthermore, the fact that there is no line search procedure incorporated in the algorithm seems to strengthen its robustness so that it tackles effectively test problems with stronger stochastic noises. The numerical results for both deterministic and stochastic test problems illustrate the appealing attributes of the algorithm.

Suggested Citation

  • W. Liu & Y. H. Dai, 2001. "Minimization Algorithms Based on Supervisor and Searcher Cooperation," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 359-379, November.
    • Handle: RePEc:spr:joptap:v:111:y:2001:i:2:d:10.1023_a:1011986402461
    DOI: 10.1023/A:1011986402461
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    References listed on IDEAS

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    1. Russell R. Barton & John S. Ivey, Jr., 1996. "Nelder-Mead Simplex Modifications for Simulation Optimization," Management Science, INFORMS, vol. 42(7), pages 954-973, July.
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    Cited by:

    1. Zhitao Xu & Li Gao, 2019. "The Uzawa-MBB type algorithm for nonsymmetric saddle point problems," Computational Optimization and Applications, Springer, vol. 73(3), pages 933-956, July.
    2. K. Sirlantzis & J. D. Lamb & W. B. Liu, 2006. "Novel Algorithms for Noisy Minimization Problems with Applications to Neural Networks Training," Journal of Optimization Theory and Applications, Springer, vol. 129(2), pages 325-340, May.
    3. Zhong-bao Wang & Xue Chen & Jiang Yi & Zhang-you Chen, 2022. "Inertial projection and contraction algorithms with larger step sizes for solving quasimonotone variational inequalities," Journal of Global Optimization, Springer, vol. 82(3), pages 499-522, March.

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