| 有界整规划中的渐近强非线性对偶 |
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| 引用本文： | 张连生,白富生.有界整规划中的渐近强非线性对偶[J].数学年刊A辑(中文版),2004(5). |
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| 作者姓名： | 张连生 白富生 |
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| 作者单位： | 上海大学数学系，上海大学数学系 上海 200436，上海 200436 |
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| 基金项目： | 国家自然科学基金(No.10271073)资助的项目. |
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| 摘 要： | 本文提出了一种整数规划中的指数一对数对偶.证明了此指数-对数对偶方法具有的渐近强对偶性质,并提出了不需要进行对偶搜索来解原整数规划问题的方法.特别地,当选取合适的参数和对偶变量时,原整数规划问题的解可以通过解一个非线性松弛问题来得到.对具有整系数目标函数及约束函数的多项式整规划问题,给出了参数及对偶变量的取法.
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| 关 键 词： | 整数规划 非线性对偶 指数-对数对偶 渐近强对偶 |
ASYMPTOTIC STRONG NONLINEAR DUALITY FOR BOUNDED INTEGER PROGRAMMING |
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| ZHANG Liansheng BAI Fusheng.ASYMPTOTIC STRONG NONLINEAR DUALITY FOR BOUNDED INTEGER PROGRAMMING[J].Chinese Annals of Mathematics,2004(5). |
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| Authors: | ZHANG Liansheng BAI Fusheng |
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| Institution: | ZHANG Liansheng BAI Fusheng
Department of Mathematics,Shanghai University,Shanghai 200436,China. Department of Mathematics,Shanghai University,Shanghai 200436,China. |
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| Abstract: | In this paper, a logarithmic-exponential dual formulation is proposed for bounded integer programming. The authors show that this dual formulation possesses an asymptotic strong duality property and no dual search is needed to solve the primal problem. Specially, it is shown that the primal problem can be solved by solving a single nonlinear relaxation problem when the parameter and the dual vector are appropriately chosen. For the polynomial integer programming problem with integer-coefficient objective function and constraint functions, the authors specify the appropriate parameter and dual vector. |
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| Keywords: | Integer programming Nonlinear duality Logarithmic-exponential dual formulation Asymptotic strong duality |
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