| 极大单调算子不精确邻近点算法的一种新的近似准则 |
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| 引用本文： | 王治华.极大单调算子不精确邻近点算法的一种新的近似准则[J].淮阴师范学院学报(自然科学版),2003,2(4):263-267. |
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| 作者姓名： | 王治华 |
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| 作者单位： | 沙洲职业工学院,基础部,江苏,张家港,215600 |
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| 摘 要： | 对于寻找极大单调算子的零点，邻近点算法(PPA)是一种重要方法．邻近点算法通过解一系列强单调的子问题产生一个序列．然而精确地解子问题太昂贵有时也不可能，在许多献里讨论了不精确邻近点算法(IPPA)．本提出了一种近似解子问题的一种新的准则，这种准则的条件比已有的准则的条件要弱，证明了这种算法在新的准则下的全局收敛性．
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| 关 键 词： | 极大单调算子 邻近点算法 非精确方法 |
| 文章编号： | 1671-6876(2003)04-0263-05 |
| 修稿时间： | 2003年6月22日 |
A New Approximation Criterion for an Inexact Proximal Point Method for Maximal Monotone Operators |
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| WANG Zhi-hua.A New Approximation Criterion for an Inexact Proximal Point Method for Maximal Monotone Operators[J].Journal of Huaiyin Teachers College(Natrual Science Edition),2003,2(4):263-267. |
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| Authors: | WANG Zhi-hua |
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| Abstract: | The proximal point algorithm (PPA) is an important method to find the zero points of maximal monotone operators. Proximal point algorithm (PPA) generates a sequence by solving a series of uniformly strongly monotone sub-problems. However, solving the sub-problems is either expensive or impossible. The inexact proximal point algorithm (IPPA) was developed in many literature. In this paper, we presented a new criterion for approximately solving sub-problems. The inexactness restrictions for convergence become milder than those presented before.The entire convergence of this algorithm under new criterion was proved. |
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| Keywords: | maximal monotone operators proximal point method inexact method |
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