解线性约束优化问题的新锥模型信赖域法(英文)  

A Trust Region Method with New Conic Model for Linearly Constrained Optimization

作　　者：陆晓平[1] 倪勤[2] 

机构地区：[1]南京航空航天大学经济与管理学院,南京210016 [2]南京航空航天大学理学院,南京210016

出　　处：《运筹学学报》2008年第4期32-42,共11页Operations Research Transactions

基　　金：supported by the National Natural Science Foundation of China (10471062);Jiangsu Province (BK2006184).

摘　　要：本文提出了一个解线性等式约束优化问题的新锥模型信赖域方法.论文采用零空间技术消除了新锥模型子问题中的线性等式约束,用折线法求解转换后的子问题,并给出了解线性等式约束优化问题的信赖域方法.论文提出并证明了该方法的全局收敛性,并给出了该方法解线性等式约束优化问题的数值实验.理论和数值实验结果表明新锥模型信赖域方法是有效的,这给出了用新锥模型进一步研究非线性优化的基础.In this paper, a trust region method with new conic model for linearly constrained optimization problems is proposed. With null space technique, linear equality constraints are deleted in the trust region subproblem. The dogleg method is used to solve the transformed subproblems. The global convergence of the method under some reasonable conditions is established and proved. A computer program based on this method has performed for test problems. The theoretical and numerical results show the efficiency of the trust region method with new conic model, and give the base of further research on nonlinear optimization by using new conic model.

关 键 词：运筹学 约束最优化 锥模型 折线法 拟牛顿算法 信赖域子问题 

分 类 号：O221.2[理学—运筹学与控制论] O224[理学—数学]