On eigenvalues induced by a cone constraint

Abstract Let A be an n×n real matrix, and K⊂ R n be a closed convex cone. The spectrum of A relative to K, denoted by σ(A,K), is the set of all λ∈ R for which the linear complementarity problem x∈K, Ax−λx∈K + , 〈x,Ax−λx〉=0 admitsa nonzero solution x∈ R n . The notation K+ stands for the (positive) dual cone of K. The purpose of this work is to study the main properties of the mapping σ(·,K), and discuss some structural differences existing between the polyhedral case (i.e. K is finitely generated) and the nonpolyhedral case.

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