A stochastic Bregman golden ratio algorithm for non-Lipschitz stochastic mixed variational inequalities with application to resource share problems

IF 2.1 2区 数学 Q1 MATHEMATICS, APPLIED
Xian-Jun Long, Jing Yang
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引用次数: 0

Abstract

In the study of stochastic mixed variational inequalities(SMVIs), Lipschitz is an indispensable assumption for the convergence analysis. However, practical applications may not satisfy this assumption. In this paper, we propose a stochastic Bregman golden ratio algorithm for solving non-Lipschitz SMVIs. Since our algorithm only requires to calculate one stochastic approximation of the expected mapping per iteration, the computations can be reduced. Under some moderate conditions, we prove the almost surely convergence of the iteration sequence and the O(1/K) convergence rate, where K denotes the maximum iteration. Furthermore, we derive the probabilities of large deviation results, which provide a high probability guarantee for the convergence of the proposed algorithm. Numerical experiments on Logistic regression problems and modified entropy regularized LP boosting problems show that our algorithm is competitive compared with some existing algorithms. Finally, we apply our algorithm to solve a non-Lipschitz resource sharing problem.
非 Lipschitz 随机混合变分不等式的随机布雷格曼黄金比率算法,应用于资源共享问题
在随机混合变分不等式(SMVI)的研究中,Lipschitz 是进行收敛分析不可或缺的假设。然而,实际应用中可能无法满足这一假设。本文提出了一种用于求解非 Lipschitz SMVI 的随机 Bregman 黄金比率算法。由于我们的算法每次迭代只需要计算一个预期映射的随机近似值,因此可以减少计算量。在一些适度条件下,我们证明了迭代序列几乎肯定收敛,收敛率为 O(1/K),其中 K 表示最大迭代次数。此外,我们还推导出了大偏差概率结果,为所提算法的收敛性提供了高概率保证。在逻辑回归问题和修正熵正则化 LP 提升问题上的数值实验表明,与一些现有算法相比,我们的算法具有很强的竞争力。最后,我们应用我们的算法解决了一个非 Lipschitz 资源共享问题。
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来源期刊
CiteScore
5.40
自引率
4.20%
发文量
437
审稿时长
3.0 months
期刊介绍: The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.
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