| 修正的IPA算法的建立及在不等式约束凸优化问题中的应用 |
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| 引用本文： | 刘文,吴庆丰,聂晓妮,程晓红.修正的IPA算法的建立及在不等式约束凸优化问题中的应用[J].数学理论与应用,2005,25(4):11-14. |
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| 作者姓名： | 刘文 吴庆丰 聂晓妮 程晓红 |
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| 作者单位： | 燕山大学理学院,秦皇岛066004 |
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| 摘 要： | 本文首先对IPA算法进行了修正，并证明了修正IPA算法的收敛性，然后将修正后的IPA应用到不等式约束凸优化问题中得到新的内点算法，并与传统的障碍函数法作了比较，从理论上体现了新算法的优势，并给出了其工程解求解法以及收敛性的证明．
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| 关 键 词： | Bregman距离 Bregman投影 IPA算法 凸优化问题 不等式约束 凸函数 |
| 收稿时间： | 03 23 2005 12:00AM |
The Establish of Modified IPA and its Applying in Convex Optimization Problems with Inequality Constraints |
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| Liu Wen Wu Qingfeng Nie Xiaoni Cheng Xiaohong.The Establish of Modified IPA and its Applying in Convex Optimization Problems with Inequality Constraints[J].Mathematical Theory and Applications,2005,25(4):11-14. |
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| Authors: | Liu Wen Wu Qingfeng Nie Xiaoni Cheng Xiaohong |
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| Institution: | Yanshan University ,Qinghuangclao, Hebei, 066004 |
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| Abstract: | In this paper,we first modify IPA and prove the convergence of the modified algorithm. Then we apply modified IPA to convex optimization problems with inequality constraints, we obtain nwe interior point algorithms and compare them with old SUMT interior point algorithms and show we the superior in the theory, we also propose the inexact methods for solving it and prove the convergence. |
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| Keywords: | Bregman distance Bregman projection IPA Convex optimization problem |
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