A new projected Barzilai-Borwein method for the symmetric cone complementarity problem

摘要

This paper presents a new projected Barzilai-Borwein method for the complementarity problem over symmetric cone by applying the Barzilai-Borwein-like steplengths to the projected method. A new descent direction is employed and a non-monotone line search is used in the method in order to guarantee the global convergence. The projected Barzilai-Borwein method is proved to be globally convergent under some suitable conditions. Some preliminary computational results are also reported which confirm the good theoretical properties of the proposed method.