An extension of the Jacobi algorithm for the complementarity problem in the presence of multivalence

Abstract

The complementarity problem is examined in the case where the basic mapping is the sum of a finite number of superpositions of a univalent off-diagonal antitone mapping and a multivalent diagonal monotone one. An extension is proposed for the Jacobi algorithm, which constructs a sequence converging to a point solution. With the use of this property, the existence of a solution to the original problem is also established. Under certain additional conditions, the minimal element in the feasible set of this problem is one of its solutions. Copyright © 2005 by MAIK "Nauka/Interperiodica".