Regularized dynamics for monotone inverse variational inequalities in hilbert spaces

IF 2 3区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

Optimization and Engineering Pub Date : 2024-03-18 DOI:10.1007/s11081-024-09882-8

Pham Ky Anh, Trinh Ngoc Hai

引用次数: 0

Abstract

In this paper, we present a regularized dynamical system method for solving monotone inverse variational inequalities (IVIs) in infinite dimensional Hilbert spaces. It is shown that the corresponding Cauchy problem admits a unique strong global solution, whose limit at infinity exists and solves the given monotone IVI. Then by discretizing the dynamical system, we obtain a class of iterative regularization algorithms with relaxation parameters, which are strongly convergent under quite mild assumptions on the cost operator. Some simple numerical examples, including an infinite dimensional one, are given to illustrate the performance of the proposed algorithms.

Abstract Image

查看原文本刊更多论文

希尔伯特空间中单调逆变不等式的正规化动力学

本文提出了一种正则化动力系统方法，用于求解无限维希尔伯特空间中的单调反变不等式（IVI）。结果表明，相应的 Cauchy 问题有一个唯一的强全局解，其在无穷远处的极限存在并能解决给定的单调 IVI。然后，通过对动力系统进行离散化处理，我们得到了一类具有松弛参数的迭代正则化算法，在对代价算子进行相当温和的假设条件下，这些算法具有很强的收敛性。我们给出了一些简单的数值例子，包括一个无限维的例子，以说明所提算法的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Optimization and Engineering 工程技术-工程：综合

CiteScore

4.80

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Optimization and Engineering is a multidisciplinary journal; its primary goal is to promote the application of optimization methods in the general area of engineering sciences. We expect submissions to OPTE not only to make a significant optimization contribution but also to impact a specific engineering application. Topics of Interest: -Optimization: All methods and algorithms of mathematical optimization, including blackbox and derivative-free optimization, continuous optimization, discrete optimization, global optimization, linear and conic optimization, multiobjective optimization, PDE-constrained optimization & control, and stochastic optimization. Numerical and implementation issues, optimization software, benchmarking, and case studies. -Engineering Sciences: Aerospace engineering, biomedical engineering, chemical & process engineering, civil, environmental, & architectural engineering, electrical engineering, financial engineering, geosciences, healthcare engineering, industrial & systems engineering, mechanical engineering & MDO, and robotics.