Variational inequality formulation of circular cone eigenvalue complementarity problems

Variational inequality formulation of circular cone eigenvalue complementarity problems

In this paper, we study the circular cone eigenvalue complementarity problem (CCEiCP) by variational inequality technique, prove the existence of a solution to CCEiCP, and investigate different nonlinear programming formulations of the symmetric and asymmetric CCEiCP, respectively. We reduce CCEiCP to a variational inequality problem on a compact convex set, which guarantees that CCEiCP has at ...

Generalized Vector Complementarity Problems With Corresponding Vector Variational Inequality Problems

In this paper, We introduce a new class of generalized vector complementarity problems and the corresponding generalized vector variational inequality problems which include many known complementarity problems and the corresponding vector variational inequality problems as special cases and establish the equivalence between those problems in Banach spaces. Furthermore, we obtain some new existe...

Some Vector Implicit Complementarity Problems with Corresponding Variational Inequality Problems

Some existence theorems of solutions of a new class of generalized vector F-implicit complementarity problems with the corresponding generalized vector F-implicit variational inequality problems were established.

The second-order cone eigenvalue complementarity problem

The Eigenvalue Complementarity Problem (EiCP) differs from the traditional eigenvalue problem in that the primal and dual variables belong to a closed and convex cone K and its dual, respectively, and satisfy a complementarity condition. In this paper we investigate the solution of the SecondOrder Cone EiCP (SOCEiCP) where K is the Lorentz cone. We first show that the SOCEiCP reduces to a speci...

Variational Formulation of Problems and Variational Methods