Convergence of the Gauss-Newton method for convex composite optimization problems under majorant condition on Riemannian manifolds

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2023-08-09 DOI:10.1016/j.jco.2023.101788

Qamrul Hasan Ansari , Moin Uddin , Jen-Chih Yao

引用次数: 1

Abstract

In this paper, we consider convex composite optimization problems on Riemannian manifolds, and discuss the semi-local convergence of the Gauss-Newton method with quasi-regular initial point and under the majorant condition. As special cases, we also discuss the convergence of the sequence generated by the Gauss-Newton method under Lipschitz-type condition, or under γ-condition.

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黎曼流形上凸复合优化问题的主要条件下高斯-牛顿法的收敛性

本文研究了黎曼流形上的凸复合优化问题，讨论了具有拟正则初始点和主要条件下高斯-牛顿方法的半局部收敛性。作为特殊情况，我们还讨论了在Lipschitz-type条件下或γ-条件下由Gauss-Newton方法生成的序列的收敛性。

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.