Abstract
By using the concept of exceptional family, we propose a sufficient condition of a solution to general order complementarity problems (denoted by GOCP) in Banach space, which is weaker than that in Németh, 2010 (Theorem 3.1). Then we study some sufficient conditions for the nonexistence of exceptional family for GOCP in Hilbert space. Moreover, we prove that without exceptional family is a sufficient and necessary condition for the solvability of pseudomonotone general order complementarity problems.
Highlights
There are several types of order complementarity problems in real world applications
By using the concept of exceptional family, we propose a sufficient condition of a solution to general order complementarity problems in Banach space, which is weaker than that in Nemeth, 2010 (Theorem 3.1)
We study some sufficient conditions for the nonexistence of exceptional family for general order complementarity problems (GOCPs) in Hilbert space
Summary
There are several types of order complementarity problems in real world applications. The concept of exceptional family is a powerful tool to study existence theorems of the solution to nonlinear complementarity problems and variational inequality problems (see [7,8,9,10,11,12,13,14,15]). In 2008, Zhang proposed an existence theorem for semidefinite complementarity problem (denoted by SDCP) He introduced generalizations of Isac-Carbone’s condition and proved that Isac-Carbone’s condition is the sufficient conditions for the solvability of SDCP (see [22]). Motivated and inspired by the works mentioned above, in this paper, by using the concept of exceptional family in [6], we propose a sufficient condition of a solution to general order complementarity problems (denoted by GOCP) in Banach space, which is weaker than that in [6, Theorem 3.1].
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