广义集值强非线性混合似变分不等式的辅助原理和三步迭代算法  

Auxiliary Principle and Three-Step Iterative Algorithms for Generalized Set-Valued Strongly Nonlinear Mixed Variational-Like Inequalities

作　　者：徐海丽[1] 郭兴明[1] 

机构地区：[1]上海大学上海市应用数学和力学研究所,上海200072

出　　处：《应用数学和力学》2007年第6期643-650,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10472061)

摘　　要：使用辅助原理技巧研究了一类广义集值强非线性混合变分不等式.证明了此类集值强非线性混合变分不等式辅助问题解的存在性和唯一性;构建了一个新的三步迭代算法,通过辅助原理技巧,构建并计算此类非线性混合变分不等式的近似解,进一步证明非线性混合变分不等式解的存在性以及由算法产生的三个序列的收敛性.所得结论推广了近年来许多混合变分不等式和准变分不等式以及他们的有关结果.The auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities was proved. A novel and innovative three-step itemtive algorithm to compute approximate solution was constructed.And the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality was showed by using the auxiliary principle technique. The convergence of three-step iterative sequences generated by the algorithm was also proved.

关 键 词：混合似变分不等式 三步迭代算法 集值映射 辅助原理技巧 

分 类 号：O177.1[理学—数学] O178[理学—基础数学]