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求解非线性系统的有效集信赖域方法
  • 期刊名称：数学物理学报26（2006），223-232
  • 时间：0
  • 分类：O221.2[理学—运筹学与控制论;理学—数学]
  • 作者机构：[1]曲阜师范大学运筹与管理学院,山东日照276826, [2]上海理工大学理学院,上海200093
  • 相关基金：国家自然科学基金（10571106）和上海理工大学博士启动基金（X529）资助
  • 相关项目：广义半无限规划的理论与算法研究
关键词： 非线性系统, 有效集信赖域方法, 截断共轭梯度法, Nonlinear system, Active-set trust region method, Truncated conjugate gradient method.
中文摘要：

该文给出了一个求解非线性系统的信赖域方法．主要思想是通过引入松弛变量，将问题等价地转化为带非负约束的最优化问题．作者利用有效集策略，在每次迭代中只需求解一个低维的信赖域子问题，该信赖域子问题是通过截断共轭梯度法来近似求解的．在较弱的条件下，获得了一个更一般的收敛性结果．

英文摘要：

In this paper, the authors present a trust region method for nonlinear system. The main idea of this paper is that by introducting slack variables, the authors transformate the problem into a nonlinear optimization with nonnegative constraints. By using active set strategy, the authors need only to solve a reduced trust region subproblem which is solved inexactly by the truncated conjugate gradient method. Under weak conditions, the authors obtain a general convergence result.

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