| 一类凸规划的多项式预估校正内点法 |
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| 引用本文： | 余谦,黄崇超,王先甲. 一类凸规划的多项式预估校正内点法[J]. 高等学校计算数学学报, 2005, 27(3): 193-201 |
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| 作者姓名： | 余谦 黄崇超 王先甲 |
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| 作者单位： | 武汉大学系统工程研究所,武汉,430072;武汉大学数学与统计学院,武汉,430072 |
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| 基金项目： | 国家自然科学基金;教育部高校骨干教师资助计划 |
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| 摘 要： | 1、引言 1990年由Mehrotra对线性规划问题提出了一个称为预估校正的方法,并在1992年给出了其数值算法．1993年Mizuno,Todd和Y．Ye．给出了改进的预估校正内点法,使得一个预估步后只跟一个校正步．1994年F．A．Potra给出了不可行预估校正内点法,使得可以从一个不可行的初始点开始算法的迭代,并证明了其为二次收敛．
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| 关 键 词： | 预估校正 内点法 多项式 凸规划 线性规划问题 数值算法 1990年 1993年 1992年 |
| 收稿时间： | 2002-09-25 |
| 修稿时间： | 2002-09-25 |
A POLYNOMIAL PREDICTOR-CORRECTOR INTERIOR-POINT ALGORITHM FOR A CLASS CONVEX PROGRAMMING |
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| Yu Qian,Huang Chongchao,Wang Xianjia. A POLYNOMIAL PREDICTOR-CORRECTOR INTERIOR-POINT ALGORITHM FOR A CLASS CONVEX PROGRAMMING[J]. Numerical Mathematics A Journal of Chinese Universities, 2005, 27(3): 193-201 |
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| Authors: | Yu Qian Huang Chongchao Wang Xianjia |
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| Abstract: | In this paper a polynomial predictor-corrector interior-point algorithm for a class convex programming with linear constrains is presented. This method is based upon a modified predictor-corrector interior-point algorithm. In this kind of algorithms there is only one corrector step after each predictor step. In each loop of our algorithm, step 2 is a predictor step and step 4 is a corrector step. At the predictor step we are trying to decrease the "dual gap" as much as possible, and at the corrector step we put iteration points back to a narrower neighborhood. It is shown that the method is a polynomial-time algorithm and has O(L) iteration complexity. |
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| Keywords: | convex programming predictor-corrector interior-point algorithm. |
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