Convergence analysis of iteratively regularized Landweber iteration with uniformly convex constraints in Banach spaces

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2024-09-13 DOI:10.1016/j.jco.2024.101897

Gaurav Mittal , Harshit Bajpai , Ankik Kumar Giri

引用次数: 0

Abstract

In Banach spaces, the convergence analysis of iteratively regularized Landweber iteration (IRLI) is recently studied via conditional stability estimates. But the formulation of IRLI does not include general non-smooth convex penalty functionals, which is essential to capture special characteristics of the sought solution. In this paper, we formulate a generalized form of IRLI so that its formulation includes general non-smooth uniformly convex penalty functionals. We study the convergence analysis and derive the convergence rates of the generalized method solely via conditional stability estimates in Banach spaces for both the perturbed and unperturbed data. We also discuss few examples of inverse problems on which our method is applicable.

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巴拿赫空间中具有均匀凸约束条件的迭代正则化 Landweber 迭代的收敛性分析

在巴拿赫空间中，最近通过条件稳定性估计研究了迭代正则化兰德韦伯迭代（IRLI）的收敛分析。但是，IRLI 的表述并不包括一般的非光滑凸惩罚函数，而这对于捕捉所求解的特殊性至关重要。在本文中，我们提出了 IRLI 的广义形式，使其表述包含一般非光滑均匀凸惩罚函数。我们研究了收敛分析，并通过巴拿赫空间中的条件稳定性估计，得出了广义方法对扰动和非扰动数据的收敛率。我们还讨论了我们的方法适用于逆问题的几个例子。

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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来源期刊

Journal of Complexity 工程技术-计算机：理论方法

CiteScore

3.10

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited. Areas Include: • Approximation theory • Biomedical computing • Compressed computing and sensing • Computational finance • Computational number theory • Computational stochastics • Control theory • Cryptography • Design of experiments • Differential equations • Discrete problems • Distributed and parallel computation • High and infinite-dimensional problems • Information-based complexity • Inverse and ill-posed problems • Machine learning • Markov chain Monte Carlo • Monte Carlo and quasi-Monte Carlo • Multivariate integration and approximation • Noisy data • Nonlinear and algebraic equations • Numerical analysis • Operator equations • Optimization • Quantum computing • Scientific computation • Tractability of multivariate problems • Vision and image understanding.