Portal de Periódicos da CAPES

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

2008; Springer Science+Business Media; Volume: 47; Issue: 4 Linguagem: Inglês

10.1007/s11075-008-9194-7

1572-9265

Joaquím J. Júdice, Marcos Raydan, Silvério Rosa, Sandra A. Santos,

Sparse and Compressive Sensing Techniques

This paper is devoted to the eigenvalue complementarity problem (EiCP) with symmetric real matrices. This problem is equivalent to finding a stationary point of a differentiable optimization program involving the Rayleigh quotient on a simplex (Queiroz et al., Math. Comput. 73, 1849–1863, 2004). We discuss a logarithmic function and a quadratic programming formulation to find 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 specially designed 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 to find a solution to the symmetric EiCP.