一类带线搜索的自适应信赖域算法  

A Self-adaptive Trust Region Algorithm with Line Search

作　　者：李红[1] 焦宝聪[1] 

机构地区：[1]首都师范大学数学科学学院,北京100037

出　　处：《运筹学学报》2008年第2期97-104,共8页Operations Research Transactions

基　　金：国家自然科学基金(60472071);北京市教委科研基金(KM200510028019)资助.

摘　　要：本文对无约束优化问题提出了一类带线搜索的自适应信赖域算法,新算法在试验步失败时不重解子问题,而是采用线搜索,从而减少了计算量,不同于一般的带线搜索的信赖域算法,新算法根据实际下降量与预估下降量的比值按照变化的速率对信赖域半径进行调整.文中在一定的条件下证明了算法的收敛性,并且给出了相应的数值实验结果.In this paper, we propose an algorithm for unconstrained optimization by employing both self-adaptive trust region and line searches. It takes line searches instead of resolving the subproblem when the trail step is not successful. This may allow a considerable computationl saving. Different from traditional trust region algorithm with line searches, the trust region radius is updated at a variable rate according to the ratio of the actual reduction to the predicted reduction of the objective function. We show that this new algorithm preserves the convergence property of traditional trust region metheods. Numeriacal results are also presented.

关 键 词：运筹学 WOLFE线搜索 信赖域方法 无约束最优化 

分 类 号：O224[理学—运筹学与控制论] TP273.2[理学—数学]