Duality for -variational inequalities via the subdifferential calculus

详细信息    查看全文

• 作者：Liana Cioban^a ; ¹ ; ^{liana.cioban@ubbcluj.ro} ; Ernö ; Robert Csetnek^b ; ^{robert.csetnek@mathematik.tu-chemnitz.de}
• 关键词：58E35 ; 47A55 ; 90C46 ; 49N15
• 刊名：Nonlinear Analysis
• 出版年：2012
• 出版时间：April 2012
• 年：2012
• 卷：75
• 期：6
• 页码：3142-3156
• 全文大小：308 K

文摘

Based on the properties of the (convex) -subdifferential calculus, we introduce to a general -variational inequality (formulated with the help of a set valued operator and a perturbation function) a dual one, expressed by making use of the (Fenchel) conjugate of the perturbation function. Under convexity hypotheses, we show that the fulfillment of a regularity condition guarantees that the primal -variational inequality is solvable if and only if its dual one is solvable. By particularizing the perturbation function, we obtain several dual statements and we succeed to generalize and improve a duality scheme recently given by Kum, Kim and Lee. An example justifying this generalization is also provided. Among the special instances of the general result, we rediscover also the duality scheme concerning variational inequalities due to Mosco.