基于锥模型的非单调信赖域算法  

A Nonmonotonic Trust Region Method the Based on the Conic Model

作　　者：刘培培[1] 焦宝聪[1] 陈兰平[1] 

机构地区：[1]首都师范大学数学科学学院,北京100037

出　　处：《数学进展》2009年第4期503-511,共9页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.60472071);北京市教委科研基金(No.KM200710028001).

摘　　要：对于无约束最优化问题本文提出了一类基于锥模型的非单调信赖域算法。此算法中的信赖域子问题是采用比二次模型更一般的锥模型,并结合非单调技术,克服了用于产生非单调性的参考函数值依赖于某一正整数M的缺点。当试探步不被接受时,采用非单调线搜索,减少了计算量。在适当的条件下,证明了该算法的全局收敛性和Q-二阶收敛性。数值试验证实该算法是有效的。In this paper, a nonmonotonic trust region algorithm based on the conic model for unconstrained optimization is presented. In this algorithm, the subproblem of trust region applys the conic model, which is more general than quadratic model. With the nonmonotonic technique, our algorithm overcomes a shortcoming, i.e. the reference function value used to generate non-monotonicity relys on some positive integer M. When the trial step is not accepted, we employ a nonmonotomic line search to reduce the cost. Under mild conditions, we prove the global convergence and Q-quadratic convergence of the algorithm. Numerical results show its efficiency.

关 键 词：无约束最优化 非单调信赖域方法 锥模型 非单调线搜索 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]