解无约束优化的非单调自适应信赖域算法

Nonmonotone Self-Adaptive Trust-region Algorithm for Solving Unconstrained Optimization

受文献[14]的启发,针对无约束优化问题提出了一个基于二次模型的非单调信赖域算法;算法结合自适应技术,避免信赖域半径更新的盲目性;并引入新的非单调技术,利用非单调Armijo线搜索得到步长,进而产生新的迭代点;在文献[14]减少一个假设条件的情况下,证明了该算法的全局收敛性,数值实验表明了算法的有效性。

Inspired by reference[ 14] ,a non-monotone trust-region algorithm is proposed based on a quaorauc model for solving unconstrained optimization. Self-adaptive technology is employed to avoid the blindness of the trust region radius＇ update. A new nonmonotone technique is introduced in this paper, a step size is got by the non- monotone Armijo line search, thus a new iterative point is achieved. The global convergence of this new algorithm is verified under the reduction of one supposed condition in reference[ 14]. Preliminary numerical experiments show that the new algorithm is effective.