一种改进的非单调自适应新锥模型信赖域算法

对无约束优化问题提出了一种改进的非单调自适应信赖域算法。尽管传统的非单调技术存在着众多优点,但是也存在着易丢失最优解等缺点,为了克服这些缺点,文中提出了一种新的非单调技术,该技术是将已成功迭代点的函数最大值与当前迭代点的函数值相结合,充分利用了目标函数的信息,进一步将这种非单调技术引入到信赖域中,提出了一种改进的非单调自适应信赖域算法,在一定的条件下,证明了算法的收敛性,数值实验表明此算法的有效性。

A Modified Nonmonotone Self-adaptive Algorithm for Trust Region of a New Conic Model

A new modified nonmonotone self-adaptive trust region algorithm is presented for unconstrained optimization problems in this paper. While the nonmonotone technique has many advantages, there are also shortcomings, such as the easy loss of the optimal solution. In order to overcome these shortcomings, this paper puts forward a new nonmonotone technique. The nonmonotone technique is introduced into the trust region and a new modified nonmonotone self-adaptive trust region algorithm is presented. With proper assumptions, we prove the global convergence of the method.