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Simple Sequential Quadratically Constrained Quadratic Programming Feasible Algorithm with Active Identification Sets for Constrained Minimax Problems

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Abstract

In this paper, the nonlinear minimax problems with inequality constraints are discussed. Based on the idea of simple sequential quadratically constrained quadratic programming algorithm for smooth constrained optimization, an alternative algorithm for solving the discussed problems is proposed. Unlike the previous work, at each iteration, a feasible direction of descent called main search direction is obtained by solving only one subprogram which is composed of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the constrained functions. Then a high-order correction direction used to avoid the Maratos effect is computed by updating the main search direction with a system of linear equations. The proposed algorithm possesses global convergence under weak Mangasarian–Fromovitz constraint qualification and superlinear convergence under suitable conditions with the upper-level strict complementarity. At last, some preliminary numerical results are reported.

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Acknowledgements

Project supported by NSFC (Grant Nos. 11271086 and 11171250), and the Natural Science Foundation of Guangxi Province (Grant No. 2011GXNSFD018022) as well as 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. School of Mathematics and Information Science, Guangxi University, Nanning, 530004, China

    Xing-de Mo & Li-juan Qiu

  3. Guangxi Technological College of Machinery and Electricity, Nanning, 530007, China

    Su-ming Yang

  4. Department of Mathematics, Taiyan Normal University, Taiyan, 030012, China

    Fu-sheng Wang

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  1. Jin-bao Jian
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  2. Xing-de Mo
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  3. Li-juan Qiu
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  5. Fu-sheng Wang
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Correspondence to Jin-bao Jian.

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Communicated by Nobuo Yamashita.

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Jian, Jb., Mo, Xd., Qiu, Lj. et al. Simple Sequential Quadratically Constrained Quadratic Programming Feasible Algorithm with Active Identification Sets for Constrained Minimax Problems. J Optim Theory Appl 160, 158–188 (2014). https://doi.org/10.1007/s10957-013-0339-z

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