不等式约束极大极小问题的一个新型模松弛强次可行SQCQP算法

doi:10.12286/jssx.2018.1.49

计算数学 ›› 2018, Vol. 40 ›› Issue (1): 49-62.DOI: 10.12286/jssx.2018.1.49

不等式约束极大极小问题的一个新型模松弛强次可行SQCQP算法

王福胜, 张瑞

太原师范学院数学系, 晋中 030619

收稿日期:2017-01-20 出版日期:2018-03-15 发布日期:2018-02-03
基金资助:
国家自然科学基金（11171250）；山西省回国留学人员科研资助项目（2017-104）资助.

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王福胜, 张瑞. 不等式约束极大极小问题的一个新型模松弛强次可行SQCQP算法[J]. 计算数学, 2018, 40(1): 49-62.

Wang Fusheng, Zhang Rui. A STRONGLY SUB-FEASIBLE NORM-RELAXED SQCQP ALGORITHM FOR THE INEQUALITY CONSTRAINED MINIMAX PROBLEMS[J]. Mathematica Numerica Sinica, 2018, 40(1): 49-62.

A STRONGLY SUB-FEASIBLE NORM-RELAXED SQCQP ALGORITHM FOR THE INEQUALITY CONSTRAINED MINIMAX PROBLEMS

Wang Fusheng, Zhang Rui

Department of Mathematics, Taiyuan Normal University, Jinzhong 030619, China

Received:2017-01-20 Online:2018-03-15 Published:2018-02-03

针对带不等式约束的极大极小问题，借鉴一般约束优化问题的模松弛强次可行SQP算法思想，提出了求解不等式约束极大极小问题的一个新型模松弛强次可行SQCQP算法.首先，通过在QCQP子问题中选取合适的罚函数，保证了算法的可行性以及目标函数F（x）的下降性，同时简化QCQP子问题二次约束项参数α_k的选取，可保证算法的可行性和收敛性.其次，算法步长的选取合理简单.最后，在适当的假设条件下证明了算法具有全局收敛性及强收敛性.初步的数值试验结果表明算法是可行有效的.

关键词： 极大极小问题, 模松弛, 强次可行, SQCQP算法, 全局收敛性

In this paper, the minimax problems with inequality constraints are discussed, and a new strongly sub-feasible norm-relaxed SQCQP algorithm for the inequality constrained minimax problems is proposed. First, the penalty function $a_k$ in the QCQP subproblem can ensure the feasibility of the algorithm and the descent property of the objective function F(x), and the parameter α_k of quadratic constraints can guarantee the feasibility and convergence of the algorithm. Second, the determination of stepsize is reasonable and simple. Finally,the proposed algorithm possesses global convergence under suitable assumptions. The preliminary numerical experiments show that the algorithm is feasible and effective.

Key words: minimax problem, Norm-relaxed, Strongly sub-feasible, SQCQP algorithm, Global convergence

MR(2010)主题分类:

90C30
65K05

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摘要

不等式约束极大极小问题的一个新型模松弛强次可行SQCQP算法

A STRONGLY SUB-FEASIBLE NORM-RELAXED SQCQP ALGORITHM FOR THE INEQUALITY CONSTRAINED MINIMAX PROBLEMS

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