求解变分包含的惯性迭代格式及其在Nash-Cournot平衡和图像恢复问题中的应用

IF 1.4 4区 数学 Q1 MATHEMATICS
Jamilu Abubakar, P. Kumam, A. I. Garba, M. Abdullahi, A. Ibrahim, K. Sitthithakerngkiet
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引用次数: 4

摘要

变分包含是一个重要的一般问题,由变分不等式、极小化问题和非线性单调方程等许多有用的问题组成。本文提出了一种求解变分包含问题的新方案,该方案使用了惯性和松弛技术。此外,该方案是自适应的,即步长不取决于底层算子的阶乘常数,而是可以使用简单的更新规则来计算。在温和条件下,对新方案生成的迭代进行了弱收敛性分析。此外,从所提出的方案中导出了求解变分不等式问题和分裂可行性问题的方案,并将其应用于求解Nash-Cournot均衡问题和图像恢复。与文献中的一些现有方案相比,实验表明了所提出的方案的实现和潜在的适用性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An inertial iterative scheme for solving variational inclusion with application to Nash-Cournot equilibrium and image restoration problems
Variational inclusion is an important general problem consisting of many useful problems like variational inequality, minimization problem and nonlinear monotone equations. In this article, a new scheme for solving variational inclusion problem is proposed and the scheme uses inertial and relaxation techniques. Moreover, the scheme is self adaptive, that is, the stepsize does not depend on the factorial constants of the underlying operator, instead it can be computed using a simple updating rule. Weak convergence analysis of the iterates generated by the new scheme is presented under mild conditions. In addition, schemes for solving variational inequality problem and split feasibility problem are derived from the proposed scheme and applied in solving Nash-Cournot equilibrium problem and image restoration. Experiments to illustrate the implementation and potential applicability of the proposed schemes in comparison with some existing schemes in the literature are presented.
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来源期刊
Carpathian Journal of Mathematics
Carpathian Journal of Mathematics MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
2.40
自引率
7.10%
发文量
21
审稿时长
>12 weeks
期刊介绍: Carpathian Journal of Mathematics publishes high quality original research papers and survey articles in all areas of pure and applied mathematics. It will also occasionally publish, as special issues, proceedings of international conferences, generally (co)-organized by the Department of Mathematics and Computer Science, North University Center at Baia Mare. There is no fee for the published papers but the journal offers an Open Access Option to interested contributors.
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