A partitioned PSB method for partially separable unconstrained optimization problems

In this paper, we propose a partitioned PSB method for solving partially separable unconstrained optimization problems. By using a projection technique, we construct a sufficient descent direction. Under appropriate conditions, we show that the partitioned PSB method with projected direction is globally and superlinearly convergent for uniformly convex problems. In particular, the unit step length is accepted after finitely many iterations. Finally, some numerical results are presented, which show that the partitioned PSB method is effective and competitive.