一类非凸规划的Peaceman-Rachford分裂法的收敛性

IF 1.9 4区数学 Q1 MATHEMATICS

Numerical Mathematics-Theory Methods and Applications Pub Date : 2021-06-01 DOI:10.4208/NMTMA.OA-2020-0063

M. Chao

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引用次数: 8

摘要

本文分析了一类具有线性约束的非凸非光滑优化问题的Peaceman-Rachford分裂方法(PRSM)的收敛性，该问题的目标函数是一个固有下半连续函数和一个强凸微分函数的和。当选择合适的惩罚参数和迭代点序列有界时，我们证明了PRSM的全局收敛性。进一步，在关联函数满足Kurdyka-Łojasiewicz性质的假设下，证明了PRSM的强收敛性。并给出了生成序列有界性的充分条件。最后，我们给出了一些初步的数值结果来证明PRSM的有效性，并与DouglasRachford分裂方法进行了比较。AMS学科分类:90C26、90C30

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Convergence of the Peaceman-Rachford Splitting Method for a Class of Nonconvex Programs

In this paper, we analyze the convergence of the Peaceman-Rachford splitting method (PRSM) for a type of nonconvex and nonsmooth optimization with linear constraints, whose objective function is the sum of a proper lower semicontinuous function and a strongly convex differential function. When a suitable penalty parameter is chosen and the iterative point sequence is bounded, we show the global convergence of the PRSM. Furthermore, under the assumption that the associated function satisfies the Kurdyka-Łojasiewicz property, we prove the strong convergence of the PRSM. We also provide sufficient conditions guaranteeing the boundedness of the generated sequence. Finally, we present some preliminary numerical results to show the effectiveness of the PRSM and also give a comparison with the DouglasRachford splitting method. AMS subject classifications: 90C26, 90C30

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来源期刊

Numerical Mathematics-Theory Methods and Applications 数学-数学

CiteScore

2.80

自引率

7.70%

发文量

审稿时长

>12 weeks

期刊介绍： Numerical Mathematics: Theory, Methods and Applications (NM-TMA) publishes high-quality original research papers on the construction, analysis and application of numerical methods for solving scientific and engineering problems. Important research and expository papers devoted to the numerical solution of mathematical equations arising in all areas of science and technology are expected. The journal originates from the journal Numerical Mathematics: A Journal of Chinese Universities (English Edition). NM-TMA is a refereed international journal sponsored by Nanjing University and the Ministry of Education of China. As an international journal, NM-TMA is published in a timely fashion in printed and electronic forms.