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

Author

Listed:
  • Jin-bao Jian

    (Yulin Normal University)

  • Xing-de Mo

    (Guangxi University)

  • Li-juan Qiu

    (Guangxi University)

  • Su-ming Yang

    (Guangxi Technological College of Machinery and Electricity)

  • Fu-sheng Wang

    (Taiyan Normal University)

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.

Suggested Citation

  • Jin-bao Jian & Xing-de Mo & Li-juan Qiu & Su-ming Yang & Fu-sheng Wang, 2014. "Simple Sequential Quadratically Constrained Quadratic Programming Feasible Algorithm with Active Identification Sets for Constrained Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 158-188, January.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:1:d:10.1007_s10957-013-0339-z
    DOI: 10.1007/s10957-013-0339-z
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    References listed on IDEAS

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    1. M. V. Solodov, 2004. "On the Sequential Quadratically Constrained Quadratic Programming Methods," Mathematics of Operations Research, INFORMS, vol. 29(1), pages 64-79, February.
    2. Fusheng Wang & Kecun Zhang, 2008. "A hybrid algorithm for nonlinear minimax problems," Annals of Operations Research, Springer, vol. 164(1), pages 167-191, November.
    3. J. B. Jian, 2006. "New Sequential Quadratically-Constrained Quadratic Programming Method of Feasible Directions and Its Convergence Rate," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 109-130, April.
    4. Jian, Jin-Bao & Tang, Chun-Ming & Zheng, Hai-Yan, 2010. "Sequential quadratically constrained quadratic programming norm-relaxed algorithm of strongly sub-feasible directions," European Journal of Operational Research, Elsevier, vol. 200(3), pages 645-657, February.
    5. E. Obasanjo & G. Tzallas-Regas & B. Rustem, 2010. "An Interior-Point Algorithm for Nonlinear Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 144(2), pages 291-318, February.
    6. 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.
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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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