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| 解新锥模型信赖域子问题的折线法 | |
| 引用本文： | 陆晓平,倪勤,刘浩. 解新锥模型信赖域子问题的折线法[J]. 应用数学学报, 2007, 30(5): 855-871 |
| 作者姓名： | 陆晓平 倪勤 刘浩 |
| 作者单位： | 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 3. 南京工业大学理学院,南京,210009 |
| 基金项目： | 国家自然科学基金;江苏省高校自然科学基金 |
| 摘 要： | 本文以新锥模型信赖域子问题的最优性条件为理论基础,认真讨论了新子问题的锥函数性质,分析了此函数在梯度方向及与牛顿方向连线上的单调性.在此基础上本文提出了一个求解新锥模型信赖域子问题折线法,并证明了这一子算法保证解无约束优化问题信赖域法全局收敛性要满足的下降条件.本文获得的数值实验表明该算法是有效的. |
| 关 键 词： | 无约束最优化 锥模型 信赖域子问题 |
| 修稿时间： | 2006-07-06 |
A Dogleg Method for Solving New Trust-region Subproblems of Conic Model |
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| LU XIAOPING,NI QIN,LIU HAO. A Dogleg Method for Solving New Trust-region Subproblems of Conic Model[J]. Acta Mathematicae Applicatae Sinica, 2007, 30(5): 855-871 | |
| Authors: | LU XIAOPING NI QIN LIU HAO |
| Affiliation: | 1.College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016;2.College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016;3.College of Science, Nanjing University of Industry, Nanjing 210009 |
| Abstract: | Based on the optimality conditions of new conic model trust-region subproblem proposed in [8], we discuss the properties of conic function of new subproblem, and analyze the monotonicity of conic function in the gradient or in the line section between gradient and Newton's direction. According to this theory a dogleg algorithm for solving new trust-region subproblems of conic model is proposed in this paper. We proved the descent condition of this algorithm which guaranteed the global convergence of trust-region method for solving unconstrained optimization problem. The numerical experiment shows that this algorithm is efficient. |
| Keywords: | unconstrained minimization conic model trust region subproblem |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ | |