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

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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.

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Acknowledgements

Project supported by NSFC (No. 11271086 and 11171250), the Natural Science Foundation of Guangxi Province (No. 2011GXNSFD018022), and Innovation Group of Talents Highland of Guangxi Higher School.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Yulin Normal University, Yulin, 537000, China

    Jin-bao Jian

  2. Luoshan Secondary Vocational School, Luoshan, 464200, China

    Qing-juan Hu

  3. College of Mathematics and Information Science, Guangxi University, Nanning, 530004, China

    Chun-ming Tang

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  1. Jin-bao Jian
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  2. Qing-juan Hu
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  3. Chun-ming Tang
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Correspondence to Jin-bao Jian.

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Jian, Jb., Hu, Qj. & Tang, Cm. Superlinearly Convergent Norm-Relaxed SQP Method Based on Active Set Identification and New Line Search for Constrained Minimax Problems. J Optim Theory Appl 163, 859–883 (2014). https://doi.org/10.1007/s10957-013-0503-5

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