| 一类Lagrangian对偶问题的零对偶间隙性质及其最优路径的收敛性 |
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| 引用本文： | 刘丙状,王长钰.一类Lagrangian对偶问题的零对偶间隙性质及其最优路径的收敛性[J].运筹学学报,2007,11(1):73-84. |
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| 作者姓名： | 刘丙状 王长钰 |
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| 作者单位： | 1. 上海大学数学系,上海,200444
2. 曲阜师范大学运筹管理学院,山东,273165 |
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| 摘 要： | 针对一般的非线性规划问题,利用某些Lagrange型函数给出了一类Lagrangian对偶问题的一般模型,并证明它与原问题之间存在零对偶间隙．针对具体的一类增广La- grangian对偶问题以及几类由非线性卷积函数构成的Lagrangian对偶问题,详细讨论了零对偶间隙的存在性．进一步,讨论了在最优路径存在的前提下,最优路径的收敛性质．
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| 关 键 词： | 运筹学 对偶间隙 Lagrangian函数 收敛性 最优路径 |
| 修稿时间： | 2006-07-10 |
Zero Duality Gap Properties for a Class of Lagrangian Dual Problem and the Convergence of Its Optimal Path |
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| Liu Bingzhuang,Wang Changyu.Zero Duality Gap Properties for a Class of Lagrangian Dual Problem and the Convergence of Its Optimal Path[J].OR Transactions,2007,11(1):73-84. |
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| Authors: | Liu Bingzhuang Wang Changyu |
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| Institution: | Department of Mathematics, Shanghai University, Shanghai 200444, China;College of Operations and Management, Qufu Normal University, Qufu 273165, China |
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| Abstract: | In this paper,we propose a general model of a class of Lagrangian dual problem for the general nonlinear programming problem with respect to some Lagrange- type functions.We obtain that the zero duality gap exists between this class of Lagrangian dual problem and the primal problem.We discuss detailedly the existence of the zero duality gap for a class of augmented Lagrangian problem,and several classes of nonlinear convolution Lagrangian dual problems.Finally,we discuss the convergence of optimal path. |
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| Keywords: | Operations research duality gap Lagrangian function convergence optimal path |
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