| 具有算子与有界约束的无穷维规划问题的最优性条件 |
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| 引用本文： | 李春发,冯恩民. 具有算子与有界约束的无穷维规划问题的最优性条件[J]. 数学研究及应用, 2004, 24(2): 257-266 |
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| 作者姓名： | 李春发 冯恩民 |
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| 作者单位： | 1. 天津理工学院经济与管理学院,天津,300191
2. 大连理工大学应用数学系,辽宁,大连,116024 |
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| 摘 要： | 本文给出了当all-at-once方法用于求解最优控制问题而产生的一类同时具有算子和对部分变量具有简单界约束的无穷维最优化问题的一个一阶必要条件,构造了相应的信赖域子问题,据此,信赖域法可以用于求解无穷空间中的最优化问题。
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| 关 键 词： | 最优控制 算子约束 信赖域法 |
| 收稿时间： | 2002-12-30 |
Optimality Condition for Infinite-dimensional Programming Problem with Operator and Bound Constraints |
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| LI Chun-fa and FENG En-min. Optimality Condition for Infinite-dimensional Programming Problem with Operator and Bound Constraints[J]. Journal of Mathematical Research with Applications, 2004, 24(2): 257-266 |
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| Authors: | LI Chun-fa and FENG En-min |
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| Affiliation: | Sch. of Econ. & Man.; Tianjin University of Technology; Tianjin; China;Dept. of Math.; Dalian University of Technology; Liaoning; China |
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| Abstract: | A first-order necessary condition for an infinite-dimensional nonlinear op- timization problem, which arises when the all-at-once method is employed to slove the optimal control problems, is formulated and analyzed. Operator constraint and simple bound on part of the variables are both considered. Based on this optimality condition, the trust-region subproblems are built, then the trust region method rnay be employed to deal with the optimizatiou problem in infinite-dimensional space. |
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| Keywords: | optimal control operator constraint trust-region method |
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