| 利用光滑型算法求解线性规划问题 |
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| 引用本文： | 孙秀萍,郑丕谔.利用光滑型算法求解线性规划问题[J].天津大学学报(自然科学与工程技术版),2008,41(7):877-883. |
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| 作者姓名： | 孙秀萍 郑丕谔 |
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| 作者单位： | [1]天津大学理学院,天津300072 [2]天津大学管理学院,天津300072 |
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| 摘 要： | 针对线性规划问题，给出了其原问题和对偶问题的最优性条件，并通过引入一个正则化的对称扰动的光滑函数，将其扩展成一个混合线性互补问题，并利用光滑型算法求解．该算法具有全局收敛的特性．对于有最优解的问题，算法能求得问题的一个严格互补解；对于不可行的问题，算法也能表明问题的不可行性．
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| 关 键 词： | 线性规划 光滑型算法 全局收敛性 严格互补解 |
Smoothing Algorithms for Solving Linear Programs |
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| SUN Xiu-ping,ZHENG Pi-e.Smoothing Algorithms for Solving Linear Programs[J].Journal of Tianjin University(Science and Technology),2008,41(7):877-883. |
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| Authors: | SUN Xiu-ping ZHENG Pi-e |
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| Institution: | SUN Xiu-ping, ZHENG Pi-e(1. School of Sciences, Tianjin University, Tianjin 300072, 2. School of Management, Tianjin University, Tianjin 300072, China; China ) |
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| Abstract: | To solve linear programs （ LP ）, the optimality conditions of original problem and the dual problem were proposed. By introducing a smoothing function with a regularized symmetrical perturbation, the optimality conditions were reformulated as a mixed linear complementary problem, which is solved by using the proposed smoothing algorithm. The proposed algorithm is shown to be globally convergent if the LP has a optimal solution, then the proposed algorithm is able to find a strictly complementary solution; and if the LP is infeasible, then the algorithm will detect infeasibility of the LP. |
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| Keywords: | linear program smoothing algorithm global convergence strictly complementary solution |
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