广义均衡问题的算法及强收敛性——基于Wiener-Hopf方程技巧

数学物理学报 ›› 2015, Vol. 35 ›› Issue (4): 695-709.

广义均衡问题的算法及强收敛性——基于Wiener-Hopf方程技巧

王月虎¹, 张从军²

1 南京财经大学管理科学与工程学院, 南京 210023;
2 南京财经大学应用数学学院, 南京 210023

收稿日期:2014-09-16 修回日期:2015-03-05 出版日期:2015-08-25 发布日期:2015-08-25
作者简介:王月虎, wyhmath8610@163.com;张从军, zcjyysxx@163.com
基金资助:
国家自然科学基金(11401296,11071109)和江苏省自然科学基金(BK20141008)资助

Strong Convergence Based on Generalized Wiener-Hopf Equation Techniques for Solving Generalized Equilibrium Problems

Wang Yuehu¹, Zhang Congjun²

1 School of Management Science and Engineering, Nanjing University of Finance and Economics, Nanjing 210023;
2 School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023

Received:2014-09-16 Revised:2015-03-05 Online:2015-08-25 Published:2015-08-25

摘要/Abstract

摘要：

利用广义 Wiener-Hopf 方程技巧构造了求解广义混合均衡问题、无限个非扩张映射的不动点问题及变分不等式问题的公共元的迭代算法, 并在 Hilbert 空间中获得了两个强收敛定理. 最后利用这些新算法研究了几类优化问题. 以上方法和结果不同于前人并且推广了 Shi 和 Noor 的结果.

关键词: 广义混合均衡问题, 算子方程技巧, 算法, 强收敛, 最优化

Abstract:

In this paper, we use generalized Wiener-Hopf equation techniques to construct an iterative scheme for generalized mixed equilibrium problems, an infinite family of non-expansive mappings and variational inequality problems. Furthermore, two strong convergence theorems are also established based on different monotonicity in Hilbert spaces. Finally, we utilize our results to study several optimization problems. The methods and results presented in this paper are different from the ones announced by many others and they extend the results of Shi and Noor.

Key words: Generalized mixed equilibrium problems, Operator equation techniques, Algorithms, Strong convergence, Optimization

中图分类号:

王月虎, 张从军. 广义均衡问题的算法及强收敛性——基于Wiener-Hopf方程技巧[J]. 数学物理学报, 2015, 35(4): 695-709.

Wang Yuehu, Zhang Congjun. Strong Convergence Based on Generalized Wiener-Hopf Equation Techniques for Solving Generalized Equilibrium Problems[J]. Acta mathematica scientia,Series A, 2015, 35(4): 695-709.

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