求解广义混合平衡问题组的迭代算法  

Iterative Algorithms for Solving the System of Generalized Mixed Equilibrium Problems

作　　者：李远秋[1] 王中宝[1] 丁协平[1] 

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2011年第2期143-149,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：四川省教育厅自然科学重点基金(2003A081)资助项目

摘　　要：在实Hilbert空间中引入和研究了包含非单调集值映象的一类新的广义混合平衡问题组的迭代算法,研究了广义Wiener-Hopf方程问题组,证明了它与广义混合平衡问题组的等价性.利用广义Wiener-Hopf方程问题组的不动点形式,提出和分析了求解广义混合平衡问题组的新的迭代算法.在此基础上,还证明了由算法生成的迭代序列强收敛于广义混合平衡问题组的解.得到的结果是新的,并且统一和推广了这一领域的最近结果.A new system of generalized mixed equilibrium problems involving non-monotone set-valued mappings is introduced and studied in real Hilbert spaces. Further, a system of generalized Wiener-Hopf equations problems is considered and its equivalence with the system of generalized mixed equilibrium problems is proved. By using a fixed point formulation of the system of generalized Wiener- Hopf equations problems, a new algorithm for solving tile generalized mixed equilibrium problems is suggested and analyzed. The iteratire sequences generated by the new algorithm converge strongly to the solution of the system of generalized mixed equilibrium problems. Our results are new and unify and generalize some recent results in this field.

关 键 词：广义混合平衡问题组 广义Wiener-Hopf方程问题组 迭代算法 HILBERT空间 

分 类 号：O117.91[理学—数学]