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. [ABSTRACT FROM AUTHOR]
In this paper, we investigate a discretized version of an elliptic optimal control problem which is presented by Stadler (2009). An alternating direction method is proposed to solve this problem and demonstrated as globally convergent. This class of methods is attractive due to its simplicity and thus is adequate for solving large-scale problems. The preliminary numerical results present the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]
In this paper, we propose a new hybrid conjugate gradient method for solving unconstrained optimization problems. The proposed method can be viewed as a convex combination of Liu–Storey method and Dai–Yuan method. An remarkable property is that the search direction of this method not only satisfies the famous D–L conjugacy condition, but also accords with the Newton direction with suitable condition. Furthermore, this property is not dependent on any line searches. Under the strong Wolfe line searches, the global convergence of the proposed method is established. Preliminary numerical results also show that our method is robust and effective. [ABSTRACT FROM AUTHOR]
Abstract: In this paper, based on a simple model of the trust region subproblem, we propose a new self-adaptive trust region method with a line search technique for solving unconstrained optimization problems. By use of the simple subproblem model, the new method needs less memory capacitance and computational complexity. And the trust region radius is adjusted with a new self-adaptive adjustment strategy which makes full use of the information at the current point. When the trial step results in an increase in the objective function, the method does not resolve the subproblem, but it performs a line search technique from the failed point. Convergence properties of the method are proved under certain conditions. Numerical experiments show that the new method is effective and attractive for large-scale optimization problems. [Copyright &y& Elsevier]