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Superlinearly Convergent Norm-Relaxed SQP Method Based on Active Set Identification and New Line Search for Constrained Minimax Problems

Author

Listed:
  • Jin-bao Jian

    (Yulin Normal University)

  • Qing-juan Hu

    (Luoshan Secondary Vocational School)

  • Chun-ming Tang

    (Guangxi University)

Abstract

In this paper, the minimax problems with inequality constraints are discussed, and an alternative fast convergent method for the discussed problems is proposed. Compared with the previous work, the proposed method has the following main characteristics. First, the active set identification which can reduce the scale and the computational cost is adopted to construct the direction finding subproblems. Second, the master direction and high-order correction direction are computed by solving a new type of norm-relaxed quadratic programming subproblem and a system of linear equations, respectively. Third, the step size is yielded by a new line search which combines the method of strongly sub-feasible direction with the penalty method. Fourth, under mild assumptions without any strict complementarity, both the global convergence and rate of superlinear convergence can be obtained. Finally, some numerical results are reported.

Suggested Citation

  • Jin-bao Jian & Qing-juan Hu & Chun-ming Tang, 2014. "Superlinearly Convergent Norm-Relaxed SQP Method Based on Active Set Identification and New Line Search for Constrained Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 859-883, December.
    • Handle: RePEc:spr:joptap:v:163:y:2014:i:3:d:10.1007_s10957-013-0503-5
    DOI: 10.1007/s10957-013-0503-5
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    References listed on IDEAS

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    1. W. Hare & J. Nutini, 2013. "A derivative-free approximate gradient sampling algorithm for finite minimax problems," Computational Optimization and Applications, Springer, vol. 56(1), pages 1-38, September.
    2. Y.H. Yu & L. Gao, 2002. "Nonmonotone Line Search Algorithm for Constrained Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 419-446, November.
    3. Fusheng Wang, 2013. "A hybrid algorithm for linearly constrained minimax problems," Annals of Operations Research, Springer, vol. 206(1), pages 501-525, July.
    4. E. Polak & R. S. Womersley & H. X. Yin, 2008. "An Algorithm Based on Active Sets and Smoothing for Discretized Semi-Infinite Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 138(2), pages 311-328, August.
    5. J. O. Royset & E. Y. Pee, 2012. "Rate of Convergence Analysis of Discretization and Smoothing Algorithms for Semiinfinite Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 855-882, December.
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    Cited by:

    1. Li, Jianling & Yang, Zhenping, 2018. "A QP-free algorithm without a penalty function or a filter for nonlinear general-constrained optimization," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 52-72.

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