A class of improved conjugate gradient methods for nonconvex unconstrained optimization

IF 1.8 3区数学 Q1 MATHEMATICS

Numerical Linear Algebra with Applications Pub Date : 2022-12-08 DOI:10.1002/nla.2482

Qingjie Hu, Hongrun Zhang, Zhijuan Zhou, Yu Chen

引用次数: 0

Abstract

In this paper, based on a new class of conjugate gradient methods which are proposed by Rivaie, Dai and Omer et al. we propose a class of improved conjugate gradient methods for nonconvex unconstrained optimization. Different from the above methods, our methods possess the following properties: (i) the search direction always satisfies the sufficient descent condition independent of any line search; (ii) these approaches are globally convergent with the standard Wolfe line search or standard Armijo line search without any convexity assumption. Moreover, our numerical results also demonstrated the efficiencies of the proposed methods.

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非凸无约束优化的一类改进共轭梯度方法

本文在Rivaie、Dai和Omer等人提出的一类新的共轭梯度方法的基础上，提出了一类改进的非凸无约束优化共轭梯度方法。与上述方法不同，我们的方法具有以下性质：（i）搜索方向总是满足与任何直线搜索无关的充分下降条件；（ii）在没有任何凸性假设的情况下，这些方法与标准Wolfe线搜索或标准Armijo线搜索是全局收敛的。此外，我们的数值结果也证明了所提出的方法的有效性。

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

Numerical Linear Algebra with Applications 数学-数学

CiteScore

3.40

自引率

2.30%

发文量

审稿时长

12 months

期刊介绍： Manuscripts submitted to Numerical Linear Algebra with Applications should include large-scale broad-interest applications in which challenging computational results are integral to the approach investigated and analysed. Manuscripts that, in the Editor’s view, do not satisfy these conditions will not be accepted for review. Numerical Linear Algebra with Applications receives submissions in areas that address developing, analysing and applying linear algebra algorithms for solving problems arising in multilinear (tensor) algebra, in statistics, such as Markov Chains, as well as in deterministic and stochastic modelling of large-scale networks, algorithm development, performance analysis or related computational aspects. Topics covered include: Standard and Generalized Conjugate Gradients, Multigrid and Other Iterative Methods; Preconditioning Methods; Direct Solution Methods; Numerical Methods for Eigenproblems; Newton-like Methods for Nonlinear Equations; Parallel and Vectorizable Algorithms in Numerical Linear Algebra; Application of Methods of Numerical Linear Algebra in Science, Engineering and Economics.