非线性等式约束优化问题的仿射信赖域方法  

An Affine Scaling Trust-Region Algorithm for Solving the Nonlinear Equality Constrained Optimization

作　　者：张勇[1] 朱德通[2] 

机构地区：[1]常州大学数理学院,江苏常州213164 [2]上海师范大学数理学院,上海200234

出　　处：《数学年刊（A辑）》2013年第4期499-512,共14页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10871130);国家教育部博士点基金(No.20093127110005)的资助

摘　　要：提出非线性等式和有界约束优化问题的结合非单调技术的仿射信赖域方法.结合信赖域方法和内点回代线搜索技术,每一步迭代转到由一般信赖域子问题产生的回代步中且满足严格内点可行条件.在合理的假设条件下,证明了算法的整体收敛性和局部超线性收敛速率.最后,数值结果表明了所提供的算法具有有效性.In this paper, the authors propose an affine scaling trust-region method in association with the nonmonotonic interior backtracking line search technique for solving the nonlinear equality constrained optimization subject to bounds on variables. By using both the trust-region strategy and the interior backtracking line search technique, each iterate switches to a backtracking step generated by the general trust-region subproblem and satisfies strict interior point feasibility by the line search backtracking technique. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. Finally, some numerical results are presented to illustrate the effectiveness of the proposed algorithm.

关 键 词：非单调技术 仿射 信赖域 

分 类 号：O221.2[理学—运筹学与控制论]