无约束优化的一类新的非单调信赖域算法

A New Nonmonotone Trust Region Algorithm of Unconstrained Optimization

当选取的初始搜索点处于峡谷附近时,利用现有的信赖域算法将搜索到的最优解可能是局部最优解。针对此问题提出了无约束优化的一类新的非单调信赖域算法。该算法是在现有的非单调信赖域算法的基础上通过放宽信赖域半径的校正条件,从而放大信赖域半径,即而可能跳出峡谷。使搜索到最优解可能是全局最优解。在一定的条件下,证明了此算法的全局收敛性,并通过数值实验验证了算法的有效性。

When the selected initial search point is near to the valley,the optimal solution searched by the existing trust region algorithms may only be the locally optimal solution.These issues are addressed and proposed a new nonmonotone trust region algorithm of unconstrained optimization,which can slack the correction conditions of the trust region radius based on the existing nonmonotone trust region algorithm and therefore enlarge the radius of trust region such that the point may jump out of the valley.This may lead to the globally optimal solution.In addition,it is proved that the algorithmpossesses the global convergence the under certain conditions.Finally,some numerical tests are made to illustrate the effectiveness of the algorithms.