Automatically Determined. Nonmonotonic Trust Region Radius Of Trust Region Algorithm

Trust region method is a kind of efficient and robust method to solve unconstrained nonlinear optimization. And the choice of the trust region radius is very important to the efficiency of the algorithm. Recently Gaidi Li[l] proposes a strategy for automatic determining the trust region radius at every iteration, which uses second order information available, and does not augment computation. Numerical results on test problems show that the strategy is effec-tive.This thesis combines two kinds of nonmonotone technique to the adaptive trust region algorithm proposed in [1]. The main goal is to study the improvement of the algorithm with the nonmonotone technique. The global convergence results of the algorithms are established. Numerical results show that the nonmonotone methods are more efficient.