Eigenvalue analysis of equilibrium processes defined by linear complementarity conditions Original Research Article

Let K be a closed convex cone in a Hilbert space (H,left angle bracket·,·right-pointing angle bracket), and let K+ be its positive dual cone. The K-eigenvalues of a continuous linear mapping A:H→H are defined via the complementarity system: xset membership, variantK, Ax−λxset membership, variantK+, left angle bracketx,Ax−λxright-pointing angle bracket=0. This paper explores two issues related to this concept: existence results, and upper bounds for the number of K-eigenvalues when the cone K is finitely generated. Special attention is devoted to the case of a Pareto cone in a finite dimensional space.