一种求解极大极小问题的灵活非单调滤子方法

doi:10.3969/j.issn.1000-1565.2020.06.001

河北大学学报(自然科学版) ›› 2020, Vol. 40 ›› Issue (6): 561-568.DOI: 10.3969/j.issn.1000-1565.2020.06.001

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一种求解极大极小问题的灵活非单调滤子方法

苏珂,林雨萌,李小川

收稿日期:2019-04-14 发布日期:2021-01-10
通讯作者: 河北省自然科学基金资助项目(A2018201172);河北省教育厅重点科研基金资助项目(ZD2015069);河北大学研究生创新项目(hbu2020ss043)
作者简介:苏珂(1978—), 女, 河北邯郸人,河北大学教授, 博士, 主要从事最优化理论和算法的研究. E-mail: suke@hbu.cn

A nonmonotone flexible filter method for minimax problems

SU Ke, LIN Yumeng, LI Xiaochuan

Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province, College of Mathematics and Information Science, Hebei University, Baoding 071002, China

Received:2019-04-14 Published:2021-01-10
Supported by:
National Natural Science Foundation of China, No.41571384, No.71433008

摘要/Abstract

摘要： 求解极大极小问题的灵活非单调滤子方法与传统的滤子方法相比,对于试探步的可接受性,该方法具有更大的灵活性,而且与单调型方法相比,计算量更小.此外,还利用一个自适应参数来调整接受准则,从而在一定程度上避免了Maratos效应.在合理的假设下,该算法具有全局收敛性,并且通过数值实验验证了该方法的有效性.

关键词: 灵活滤子方法, 极大极小问题, 非单调, 信赖域, 全局收敛

Abstract: A nonmonotone flexible filter method for minimax problems is proposed. This new method has more flexibility for the acceptance of the trial step compared to the traditional filter methods, and requires less computational costs compared with the monotone-type methods. Moreover, we use a self-adaptive parameter to adjust the acceptance criteria, so that Maratos effect can be avoided to a certain degree. Under reasonable assumptions, the proposed algorithm is globally convergent. Numerical tests are presented that confirm the efficiency of the approach.

Key words: flexible filter method, minimax problem, nonmonotone, trust region, global convergence

中图分类号:

O221.2

苏珂,林雨萌,李小川. 一种求解极大极小问题的灵活非单调滤子方法[J]. 河北大学学报(自然科学版), 2020, 40(6): 561-568.

SU Ke, LIN Yumeng, LI Xiaochuan. A nonmonotone flexible filter method for minimax problems[J]. Journal of Hebei University(Natural Science Edition), 2020, 40(6): 561-568.

参考文献

[1] HAN S P. Variable metric methods for minimizing a class of nondifferentiable functions[J]. Mathematical Programming, 1981, 20(1): 1-13. DOI:10.1007/BF01589328.
[2] OSBORNE M R, WATSON G A. An algorithm for minimax approximation in the nonlinear case[J]. Computer Journal, 1969, 12(1): 63-68. DOI:10.1093/comjnl/12.1.63.
[3] ZHANG J L. A robust trust region method for nonlinear optimization with inequality constraint[J]. Applied Mathematics and Computation, 2006, 176(2): 688-699. DOI:10.1016/j.amc.2005.10.015.
[4] NOCEDAL J, WRIGHT S. Numerical optimization[M]. New York: Springer, 1999.
[5] FLETCHER R, LEYFFER S. Nonlinear programming without a penalty function[J]. Mathematical Programming, 2002, 91(2): 239-269. DOI:10.1007/s101070100244.
[6] CHIN C M, FLETCHER R. On the global convergence of an SLP-filter algorithm that takes EQP steps[J]. Mathematical Programming, 2003, 96(1): 161-177. DOI:10.1007/s10107-003-0378-6.
[7] FLETCHER R, GOULD N, LEYFFER S, et al. Global convergence of a trust region SQP filter algorithm for general nonlinear programming[J]. SIAM Journal on Optimization, 2002,13(3): 635-659. DOI:10.1137/S1052623499357258.
[8] FLETCHER R, LEYFFER S, TOINT P L. On the global convergence of a filter-SQP algorithm[J]. SIAM Journal on Optimization, 2002, 13(1): 44-59. DOI:10.1137/S105262340038081X.
[9] ULBRICH M, ULBRICH S, VICENTE L N. A globally convergent primal-dual interior-point filter method for nonlinear programming[J]. Mathematical Programming, 2004, 100(2): 379-410. DOI:10.1007/s10107-003-0477-4.
[10] AUDET C, DENNIS J E. A pattern search filter method for nonlinear programming without derivatives[J]. SIAM Journal on Optimization, 2004, 14(4): 980-1010. DOI:10.1137/S105262340138983X.
[11] KARAS E, RIBEIRO A, SAGASTIZÁBAL C, et al. A bundle filter method for nonsmooth convex constrained optimization[J]. Mathematical Programming, 2009, 116(1/2): 297-320. DOI:10.1007/s10107-007-0123-7.
[12] ULBRICH M, ULBRICH S. Non-monotone trust region methods for nonlinear equality constrained optimization without a penalty function[J]. Mathematical Programming, 2003, 95(1): 103-135. DOI:10.1007/s10107-002-0343-9.
[13] ULBRICH S. On the superlinear local convergence of a filter-SQP method[J]. Mathematical Programming, 2004, 100(1): 217-245. DOI:10.1007/s10107-003-0491-6.
[14] NIE P Y, MA C F. A trust region filter method for general non-linear programming[J]. Applied Mathematics and Computation, 2006, 172(2): 1000-1017. DOI:10.1016/j.amc.2005.03.004.
[15] ZHAO Q, GUO N. A nonmonotone filter method for minimax problems[J]. Applied Mathematics, 2011, 2(11): 1372-1377. DOI:10.4236/am.2011.211193.
[16] HU Q J, HU J Z. A sequential quadratic programming algorithm for nonlinear minimax problems[J]. Bulletin of the Australian Mathematical Society, 2007, 76(3): 353-368. DOI:10.1017/S0004972700039745.
[17] 苏珂,任乐乐,荣自兴,等.无约束优化的修正非单调记忆梯度法[J].河北大学学报(自然科学版),2018,38(6):561-566. DOI:10.3969/j.issn.1000-1565.2018.06.001.
[18] SU K, PU D G. A nonmonotone filter trust region method for nonlinear constrained optimization[J]. Journal of Computation and Applied Mathematics, 2009, 223(1): 230-239. DOI:10.1016/j.cam.2008.01.013.

一种求解极大极小问题的灵活非单调滤子方法

A nonmonotone flexible filter method for minimax problems

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