求解一类非凸变分不等式的近似点算法  

On a Proximal Point Algorithm for Solving a Class of Nonconvex Variational Inequalities

作　　者：殷羽[1] 

机构地区：[1]重庆工商大学派斯学院,重庆合川401520

出　　处：《西南师范大学学报（自然科学版）》2015年第8期29-32,共4页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：重庆市自然科学基金项目(CSTC2012jjA00039);重庆市教委科技研究项目(KJ130712;KJ1400614)

摘　　要：介绍和考虑了一类新的非凸变分不等式,这类变分不等式包括了一些已知的和新的非凸变分不等式作为特例.利用一致r-近似正规集的概念,建立了这类变分不等式和不动点问题的等价关系.利用该等价关系,给出了一个求解此类非凸变分不等式的近似点算法,并证明了该算法在适当的条件下收敛.This paper introduces and considers a new class of nonconvex variational inequalities .T his class of variational inequalities includes some know n and new nonconvex variational inequalities as special cases . Relying on the γ‐prox‐regularity notion ,we have established the equivalence between the variational ine‐qualities and the fixed point problems .By means of the equivalence ,we suggest and analyze a proximal point algorithm for solving this nonconvex variational inequalities .The new algorithm converges under certain mild conditions .As a consequence ,the algorithm and results presented in the paper overcome incor‐rect algorithms and results existing in the literature [1] .Our results can also be viewed as a novel and im‐portant extension and improvement of the previously known results .

关 键 词：非凸变分不等式 近似正规锥 强单调 投影技巧 

分 类 号：O177.91[理学—数学]