The bounded smooth reformulation and a trust region algorithm for semidefinite complementarity problems

摘要

In this paper, we present a new merit function for the semidefinite complementarity problem (SDCP) by extending the bounded smooth reformulation for variational inequality problems. We prove that the merit function has a bounded level set and any stationary point of it is a global minimizer without the assumption of monotonicity. Moreover, we present a trust region algorithm for solving the minimization problem with semidefinite constraints. The trust region subproblem is solved by the truncated conjugate gradient method and the global convergence is established even without requiring the existence of an accumulation point of the generated sequence.