| 有限维逼近无限维总极值的积分型方法 |
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| 引用本文： | 贺真真,崔洪泉,郑权. 有限维逼近无限维总极值的积分型方法[J]. 运筹学学报, 2005, 9(1): 21-31 |
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| 作者姓名： | 贺真真 崔洪泉 郑权 |
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| 作者单位： | 1. 上海大学数学系,上海,200444
2. 上海大学数学系,上海,200444;Columbus State University,Columbus,GA 31907,USA |
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| 摘 要： | 本文用有限维逼近无限维的方法来讨论函数空间中的总体最优化问题．我们给出了新的最优性条件和用变测度方法求得的有限维解逼近总体最优解的算法．对于有约柬问题，我们用不连续罚函数法把有约束问题化为无约束问题来求解．最后，我们通过一个具有非凸状态约束的最优控制问可题的实例来说明算法的有效性．
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| 关 键 词： | 无限维 有限维 总极值 逼近 最优性条件 积分 函数空间 测度方法 有效性 问题 |
Finite Dimensional Approximation to Global Minima - An Integral Approach |
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| He Zhenzhen,Cui Hongquan,Zheng Quan. Finite Dimensional Approximation to Global Minima - An Integral Approach[J]. OR Transactions, 2005, 9(1): 21-31 |
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| Authors: | He Zhenzhen Cui Hongquan Zheng Quan |
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| Affiliation: | He Zhenzhen Cui Hongquan Zheng Quan Department of Mathematics,Shanghai University,Shanghai 200444,China, Columbus State University,Columbus,GA 31907,USA . |
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| Abstract: | New optimality conditions of the integral global minimization are applied to characterize global minimum in functional space as a sequence of approximating solutions in finite-dimensional spaces. A variable measure algorithm is used to find such solutions. For a constrained problem, a discontinuous penalty method is proposed to convert it to unconstrained ones. A numerical example on optimal control problem with non convex state constraints is given to show that the algorithm is efficient. |
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| Keywords: | Operations research optimality conditions integral global minimization variable measure finite Dimensional approximation |
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