一类约束优化问题的非单调信赖域算法

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-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.

A Class of Nonmonotone Trust Region Algorithm for Constrained Optimization

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 defi...