| 求解大型线性规划的无约束化方法 |
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| 引用本文： | 卢新明. 求解大型线性规划的无约束化方法[J]. 山东科技大学学报(自然科学版), 1992, 0(1) |
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| 作者姓名： | 卢新明 |
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| 作者单位： | 山东矿业学院应用数学与软件工程系 |
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| 摘 要： | 在本文中,基于对偶理论,把线性规划变成了求解一个凸函数的无约束极小化问题。然后利用共轭梯度法求解该问题,在这个共轭梯度法中,采用了一个非常有效的一维搜索技术。理论分析和数值实验表明在一般条件下,该方法仅需要O(n)次迭代。这里n是变量个数。
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| 关 键 词： | 线性规划 大规模问题 对偶理论 共轭梯度法 退化 |
AN UNCONSTRAINED OPTIMIZATION METHOD FOR SOLVING LARGE SCALE LINEAR PROGRAMMING |
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| Lu Xinming. AN UNCONSTRAINED OPTIMIZATION METHOD FOR SOLVING LARGE SCALE LINEAR PROGRAMMING[J]. Journal of Shandong Univ of Sci and Technol: Nat Sci, 1992, 0(1) |
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| Authors: | Lu Xinming |
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| Affiliation: | Dept. of Appl. Math. & Software Eng. |
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| Abstract: | In this paper, we, based on the dual theorg, change the linear programming into the unconstrained minimization problem of a convex function Then, we solve this problem using the conjugate gradient method. In this conjugate gradient method, we adopt a very efficient technigue of one dimensional search. The theoretical analysis and the numerical experiments demonstrate that the method only needs O(n) iterations under general conditions, in which n is the number of variables. |
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| Keywords: | linear programming large scale problem dual theory conjugate gradient method degeneracy |
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