Hadamard空间中改进的近点算法。

IF 1.6 3区数学 Q1 Mathematics Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-05-24 DOI:10.1186/s13660-018-1713-z

Shih-Sen Chang, Lin Wang, Ching-Feng Wen, Jian Qiang Zhang

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引用次数: 4

摘要

本文的目的是提出一种改进的近点算法来求解Hadamard空间中的最小化问题。然后，我们证明了算法生成的序列强收敛(收敛于度量)到凸目标函数的最小值。所得结果推广了Hilbert空间、Hadamard流形和非正曲率度量空间中的若干结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The modified proximal point algorithm in Hadamard spaces.

The purpose of this paper is to propose a modified proximal point algorithm for solving minimization problems in Hadamard spaces. We then prove that the sequence generated by the algorithm converges strongly (convergence in metric) to a minimizer of convex objective functions. The results extend several results in Hilbert spaces, Hadamard manifolds and non-positive curvature metric spaces.

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来源期刊

Journal of Inequalities and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.30

自引率

6.20%

发文量

136

审稿时长

3 months

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.