An extension of the auxiliary problem principle to variational inequalities with non-symmetric multi-valued operators in Hilbert spaces is studied. This extension supposes that the operator of the variational inequali...
详细信息
An extension of the auxiliary problem principle to variational inequalities with non-symmetric multi-valued operators in Hilbert spaces is studied. This extension supposes that the operator of the variational inequality is split up into the sum of a maximal monotone operator Q and a single-valued operator F, which is linked with a sequence {L-k} of non-symmetric components of auxiliary operators by a kind of pseudo Dunn property. The current auxiliary problem is constructed by fixing T at the previous iterate, whereas Q is considered at a variable point. Using auxiliary operators of the form L-k + chi(k)delh, with chi(k) > 0, the standard assumption of the strong convexity of the function h is weakened by exploiting mutual properties of Q and h. Convergence of the general scheme is analysed allowing that the auxiliary problems are solved approximately. Some applications are sketched briefly.
暂无评论