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

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.