有关广义均衡和非扩张映射新的迭代方法
首发时间:2009-11-09
摘要:最近几年来,均衡问题成为研究的热点,因为其应用范围非常广泛,特别是在最优化和变分不等式上问题上有独特的优势。后来,广义均衡也被提出并被研究和发展。本文的目的是在希尔伯特空间引入一种新的迭代方法,来寻找广义均衡问题和有限组非扩张的不动点集的公共元素,并进一步证明给出的迭代强收敛到变分不等式的唯一解,同时也强收敛到最小值问题的最优解。同时推广和改进了Tada and Takahashi等人相应的结果。
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a new iterative method about equilibrium problem and nonexpansive mappings
Abstract:Recently,the equilibrium problem is becoming the hot topic,because of its wide applications,especially in optimization and variational inequalities. Later,the generalied equilibrium problem is given and being researched.The purpose of this article is to introduce an iterative method for finding a common element of the set of solutions of a generalized equilibrium problem and of the set of fixed points of a finite family of nonexpansive mappings in a Hilbert space.We prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality,which is the optimality condition for a minimization problem.
Keywords: Inverse-strongly monotone mapping Generalized equilibrium problem variational inequality iterative algorithm
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