一类约束优化问题的非单调信赖域算法

A Class of Nonmonotone Trust Region Algorithm for Constrained Optimization

本文就一类等式约束优化问题,结合当前比较流行的非单调技术,提出了一类新的求解等式约束优化的非单调信赖域算法.其非单调程度由算法自适应控制,计算预测下降量和实际下降量的比值时,采用前m(k)个点的信息,这不同于以前在计算预测下降量和实际下降量的比值时,仅仅采用当前一个点的信息.在没有正则性条件的假设下我们证明了算法是有定义的.并且通过对不同情况的讨论证明了算法的全局收敛性.基本的数值试验表明算法是有效的,且说明提出的非单调信赖域算法比单调信赖域算法有效.

This thesis combines the nonmonotone technique and proposes a nonmonotone trust region algorithm to solve equality constrained optimization.The nomnonotone degree is controlled by algorithm self-adapt,when we calculate the ratio of predicted reduction and actual reduction,we adopt the information of the frontal m_（（k））dots.It is differ from previously adopted the information of the frontal a dot when we calculate the ration of predicted reduction and actual reduction.We prove that the algorithm is well defined and the global convergence of method is obtained without regular conditions.Preliminary numerical results show the algorithm is effective,and nonmonotone trust region algorithm is more effective than monotone trust region algorithm.