广义集值强非线性混合似变分不等式解的迭代逼近  

ITERATIVE APPROXIMATION OF SOLUTIONS TO GENERALIZED SET-VALUED STRONGLY NONLINEAR MIXED VARIATIONAL-LIKE INEQUALITIES

作　　者：曾六川[1] 

机构地区：[1]上海师范大学数学系,上海200234

出　　处：《系统科学与数学》2006年第5期629-640,共12页Journal of Systems Science and Mathematical Sciences

基　　金：国家教育部高等学校优秀青年教师教学和科研奖励基金;上海市教委重点学科经费(部分)及上海市重点学科经费(04010)资助.

摘　　要：延拓辅助原理的技巧研究一类取非紧值的集值映象的广义强非线性混合似变分不等式．证明了这类广义强非线性混合似变分不等式的辅助问题解的存在性．利用该存在性结果,给出了解这类广义强非线性混合似变分不等式的迭代算法,最终证明了这类广义强非线性混合似变分不等式解的存在性及由算法生成的迭代序列的收敛性．The auxiliary principle technique is extended to study a class of generalized strongly nonlinear mixed variational-like inequalities for set-valued mappings without compact values. Firstly, the existence of solutions to the auxiliary problems for this class of generalized strongly nonlinear mixed variational-like inequalities is shown. Secondly, the iterative algorithm for solving this class of generalized strongly nonlinear mixed variational-like inequalities is given by using this existence result. Finally, not only the existence of solutions of this class of generalized strongly nonlinear mixed variational-like inequalities is shown, but also the convergence of iterative sequences generated by the algorithm is proven.

关 键 词：混合似变分不等式 辅助原理的技巧 迭代算法 集值映象 存在性 收敛性 

分 类 号：O177[理学—数学]