The descent algorithm for solving the symmetric eigenvalue complementarity problem

In this paper, we introduce the difference of convex function (DC) algorithm and the descent algorithm for solving the symmetric eigenvalue complementarity problem (EiCP), respectively. The main effort of these two algorithms is to efficiently find a stationary point of a quadratic subproblem in each iteration. Moreover, the global convergence of the proposed algorithms is discussed. Numerical experiments show the advantage of our proposed algorithms over several state-of-the-art solvers, such as an alternating direction method of multipliers (ADMM) and the sequential partial linearization (SPL) algorithms.