On the solution of the symmetric eigenvalue complementarity problem by the spectral projected gradient algorithm

This paper is devoted to the Eigenvalue Complementarity Problem (EiCP) with symmetric real matrices. This problem was shown to be equivalent to finding a stationary point of a differentiable optimization program involving the Rayleigh quotient on a simplex [22]. We discuss a logarithmic function and a quadratic programming formulation for finding a complementarity eigenvalue by computing a stationary point of an appropriate merit function on a special convex set. A variant of the spectral projected gradient algorithm with a suitable exact line search is introduced to solve the EiCP. Computational experience shows that the application of this algorithm to the logarithmic function formulation is a quite efficient way for finding a solution to the symmetric EiCP.