A block Lanczos method for the symmetric generalized eigenvalue complementarity problem

This paper concerns with the symmetric generalized eigenvalue complementarity problem (GEiCP) in large-scale settings. A block Lanczos method is presented in this paper to solve the symmetric GEiCP, based on the fact that a large-scale symmetric GEiCP is equivalent to its corresponding small-scale symmetric GEiCP at the event of the exact breakdown of the block Lanczos projection process. The quadratically constrained quadratic programming (QCQP) formulation is employed to solve the small-scale symmetric GEiCP for an approximate solution to the original symmetric GEiCP. The convergence analysis is presented for the case in which the block Lanczos projection process experiences no breakdown, and the convergence rate of the block Lanczos method for solving GEiCP is elaborated in detail. We compare three types of QCQP solvers based on the block Lanczos method, and numerical results demonstrate the efficiency of the block Lanczos method in solving the symmetric GEiCP.