带回溯线搜索步的双子问题信赖域算法  

A Trust-region Method with Two Subproblems and Backtracking Line Search

作　　者：唐明筠[1] 

机构地区：[1]中国农业大学理学院,北京100083

出　　处：《工程数学学报》2010年第4期627-636,共10页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10831006);中国科学院知识创新工程(kjcx-yw-s7-03)~~

摘　　要：无约束非线性优化问题广泛存在于工程、科学计算等实际应用领域。本文在信赖域算法的框架下提出无约束子问题,将它与信赖子问题相结合,构造了求解无约束优化问题的双子问题信赖域算法。同时利用信赖域子问题得到的试探步一定是目标函数充分下降方向的性质使得每次求解信赖域子问题之后均能得到使目标函数下降的步。在标准假设下证明了该算法具有全局收敛性和局部二次收敛速度。数值结果表明该算法比传统的信赖域算法速度更快更有效。Unconstrained optimization problems occur frequently in many real world applications such as engineering and scientific computing. Under the trust-region framework, we combine an un- constrained subproblem with a trust-region subproblem, and propose a trust-region method with two subproblems for solving unconstrained optimization. A backtracking line search is carried out if the trust-region trail step fails since there is always a suffcient descent direction for the objective function. The global convergence and the local quadratic convergence rate are proved under standard assump- tions. Numerical results show that this algorithm is reliable and more effcient.

关 键 词：无约束优化 信赖域方法 双子问题 回溯 收敛性 

分 类 号：O221.2[理学—运筹学与控制论]