A Class of Second-Order Cone Eigenvalue Complementarity Problems for Higher-Order Tensors

On the cone eigenvalue complementarity problem for higher-order tensors

In this paper, we consider the tensor generalized eigenvalue complementarity problem (TGEiCP), which is an interesting generalization of matrix eigenvalue complementarity problem (EiCP). First, we give an affirmative result showing that TGEiCP is solvable and has at least one solution under some reasonable assumptions. Then, we introduce two optimization reformulations of TGEiCP, thereby benefi...

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...

Higher-degree eigenvalue complementarity problems for tensors

In this paper, we introduce a unified framework of Tensor Higher-Degree EigenvalueComplementarity Problem (THDEiCP),which goes beyond the framework of the typical Quadratic Eigenvalue Complementarity Problem for matrices. First, we study some topological properties of higher-degree cone eigenvalues of tensors. Based upon the symmetry assumptions on the underlying tensors, we then reformulate TH...

An efficient algorithm for second-order cone linear complementarity problems

Recently, the globally uniquely solvable (GUS) property of the linear transformation M ∈ Rn×n in the second-order cone linear complementarity problem (SOCLCP) receives much attention and has been studied substantially. Yang and Yuan [30] contributed a new characterization of the GUS property of the linear transformation, which is formulated by basic linear-algebra-related properties. In this pa...

forSe ond - Order - Cone Complementarity Problems