A sequential partial linearization algorithm for the symmetric eigenvalue complementarity problem

Abstract

In this paper, we introduce a Sequential Partial Linearization (SPL) algorithm for finding a solution of the symmetric Eigenvalue Complementarity Problem (EiCP). The algorithm can also be used for the computation of a stationary point of a standard fractional quadratic program. A first version of the SPL algorithm employs a line search technique and possesses global convergence to a solution of the EiCP under a simple condition related to the minimum eigenvalue of one of the matrices of the problem. Furthermore, it is shown that this condition is verified for a simpler version of the SPL algorithm that does not require a line search technique. The main computational effort of the SPL algorithm is the solution of a strictly convex standard quadratic problem, which is efficiently solved by a finitely convergent block principal pivoting algorithm. Numerical results of the solution of test problems from different sources indicate that the SPL algorithm is in general efficient for the solution of the symmetric EiCP in terms of the number of iterations, accuracy of the solution and total computational effort.