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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2018, Vol. 35 ›› Issue (5): 601-610.doi: 10.3969/j.issn.1005-3085.2018.05.011

• • 上一篇    

稳固非扩张映射不动点集处均衡问题的一种不精确次梯度算法（英）

党亚峥,   刘雯雯   

  1. 上海理工大学管理学院，上海  200093
  • 收稿日期:2016-10-24 接受日期:2017-03-06 出版日期:2018-10-15 发布日期:2018-12-15
  • 基金资助:
    上海市自然科学基金(14ZR1429200)；上海市教委创新项目(15ZZ073).

A New Inexact Subgradient Algorithm for the Equilibrium Problem over the Fixed Point Set of a Firmly Nonexpansive Mapping

DANG Ya-zheng,   LIU Wen-wen   

  1. School of Management, University of Shanghai for Science and Technology, Shanghai 200093
  • Received:2016-10-24 Accepted:2017-03-06 Online:2018-10-15 Published:2018-12-15
  • Supported by:
    The Natural Science Foundation of Shanghai (14ZR1429200); the Innovation Program of Shanghai Municipal Education Commission (15ZZ073).

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摘要： 本文提出了稳固非扩张映射不动点集处均衡问题的一种新算法．该算法要求双函数是连续的，但不一定是单调的．首先，通过事先引入的参数确定一个闭凸集；其次，根据双函数的不精确次梯度在闭凸集上的投影构造中间迭代点；最后，下一个迭代点由当前迭代点和中间迭代点的凸组合在稳固非扩张算子的映射得到．在适当条件下，本文给出了该算法的全局收敛性证明．

关键词: 均衡问题, 稳固非扩张映射, 不精确次梯度算法, 全局收敛性

Abstract: In this paper, we present a new method for solving equilibrium problem over the fixed point set of a firmly nonexpansive mapping, where the underlying bifunction is continuous but not necessarily monotone. Firstly, we construct a closed ball by introducing some parameters. Then, we calculate the intermediate iterate by the projection of the inexact subgradient onto the closed convex set. The next iterate is obtained as the firmly nonexpansive mapping of a convex combination, which consists of the current iterate and the intermediate iterate. Finally, we analyse the convergence properties and the global convergence of the algorithm under some suitable conditions.

Key words: equilibrium problem, firmly nonexpansive mapping, inexact subgradient algorithm global convergence

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