一类新的广义非凸变分不等式问题的近似解  

Approximate solution for a new class of general nonconvex variational inequality problems

作　　者：闻道君[1] 万波[1] 

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《云南大学学报（自然科学版）》2014年第1期1-5,共5页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(11001287);重庆市自然科学基金(CSTC 2012jjA00039);重庆市教委科技研究(KJ130712;KJ130731)

摘　　要：引入了一类新的广义非凸变分不等式,利用投影技巧建立该变分不等式与不动点问题的等价关系,进一步讨论逼近广义非凸变分不等式解的预测-校正投影算法,并在算子T具有g-γ-强单调性的条件下证明了相应迭代序列收敛到广义非凸变分不等式问题的解.A new class of extended general nonconvex variational inequalities is introduced. The equivalence between the extended general nonconvex variational inequality and the fixed point problem is established using essentially projection technique. This alternative equivalent formulation is used to suggest and analyze a predictor - corrector method for finding an approximate solution of the general nonconvex variational inequality. The con- vergence analysis of the corresponding iterative sequence are also considered under the condition of the underly- ing operator T with g - T - strongly monotone.

关 键 词：广义非凸变分不等式 预测-校正方法 近似正规锥 g—γ-强单调 μ-Lipschitz连续 

分 类 号：O177.91[理学—数学]