A New Active Set Trust-region Algorithm For Box Constrained Optimization

In this paper, we propose a new active set trust-region algorithm for box constrained optimization, which alternates between the projected gradient step along the arc and trust-region step, with the aid of a delicate active set strat-egy. In projected gradient step, we first get the descended direction, then by the projection line search produce new iteration points, and on the basis of dCk in the trust region step, we choose the appropriate search direction dk by conjugate gra-dient method. Our algorithm have both global convergence and local convergence. We show that any accumulation point of the algorithm is a stationary point, and the algorithm will only perform the trust region steps after finite iterations under the condition that the accumulation point satisfies the second-order sufficient op-timality condition. Numerical experiments are provided to show the efficiency of our algorithm for large-scale box constrained problems, compared with the state-of-art algorithm for box constrained minimization problem by trust region method without active set strategy.