一个基于 BFGS 更新的惯性三项共轭梯度投影法

Abstract

Abstract:

Based on the BFGS update, in this paper, we present a class of improved three-term search directions. Then, by combining the inertial strategy and hyperplane projection approach, an inertial three-term conjugate gradient projection method is proposed for solving unconstrained nonlinear monotone equations. The proposed inertial algorithm exhibits the following features: (i) its search direction always possesses sufficient descent and trust region properties, independent of any line search; (ii) the inertial strategy generates iterative points by utilizing information from three iterations; (iii) the method achieves global convergence results without assuming the underlying mapping to satisfy Lipschitz continuity. Preliminary numerical experiments verify the effectiveness of the proposed method.

Key words: nonlinear monotone equations, three-term conjugate gradient method, inertial strategy, BFGS Update, global convergence

CLC Number:

O221.2

Pengjie Liu, Hu Shao, Jiayi Li, Duanduan Dong. An Inertial Three-Term Conjugate Gradient Projection Method Based on BFGS Update[J].Acta mathematica scientia,Series A, 2025, 45(5): 1698-1710.

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An Inertial Three-Term Conjugate Gradient Projection Method Based on BFGS Update

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