The notion of “exceptional family of elements (EFE)” plays a very important role in solving complementarity prob- lems. It has been applied in finite dimensional spaces and Hilbert spaces by many authors. In this pa...The notion of “exceptional family of elements (EFE)” plays a very important role in solving complementarity prob- lems. It has been applied in finite dimensional spaces and Hilbert spaces by many authors. In this paper, by using the generalized projection defined by Alber, we extend this notion from Hilbert spaces to uniformly smooth and uniformly convex Banach spaces, and apply this extension to the study of nonlinear complementarity problems in Banach spaces.展开更多
This paper introduces a new concept of exceptional family forvariational inequality problems with a general convex constrained set. By using this new concept, the authors establish a general sufficient condition for t...This paper introduces a new concept of exceptional family forvariational inequality problems with a general convex constrained set. By using this new concept, the authors establish a general sufficient condition for the existence of a solution to the problem. This condition is weaker than many known solution conditions and it is also necessary for pseudomonotone variational inequalities. Sufficient solution conditions for a class of nonlinear complementarity problems with P0 mappings are also obtained.展开更多
文摘The notion of “exceptional family of elements (EFE)” plays a very important role in solving complementarity prob- lems. It has been applied in finite dimensional spaces and Hilbert spaces by many authors. In this paper, by using the generalized projection defined by Alber, we extend this notion from Hilbert spaces to uniformly smooth and uniformly convex Banach spaces, and apply this extension to the study of nonlinear complementarity problems in Banach spaces.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19731001) .
文摘This paper introduces a new concept of exceptional family forvariational inequality problems with a general convex constrained set. By using this new concept, the authors establish a general sufficient condition for the existence of a solution to the problem. This condition is weaker than many known solution conditions and it is also necessary for pseudomonotone variational inequalities. Sufficient solution conditions for a class of nonlinear complementarity problems with P0 mappings are also obtained.
