An Improved Three-Term Conjugate Gradient Algorithm for Constrained Nonlinear Equations under Non-Lipschitz Conditions and Its Applications

Dandan Li, Yong Li and Songhua Wang ()
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Dandan Li: School of Artificial Intelligence, Guangzhou Huashang College, Guangzhou 511300, China
Yong Li: School of Mathematics, Physics and Statistics, Baise University, Baise 533099, China
Songhua Wang: School of Mathematics, Physics and Statistics, Baise University, Baise 533099, China

Mathematics, 2024, vol. 12, issue 16, 1-22

Abstract: This paper proposes an improved three-term conjugate gradient algorithm designed to solve nonlinear equations with convex constraints. The key features of the proposed algorithm are as follows: (i) It only requires that nonlinear equations have continuous and monotone properties; (ii) The designed search direction inherently ensures sufficient descent and trust-region properties, eliminating the need for line search formulas; (iii) Global convergence is established without the necessity of the Lipschitz continuity condition. Benchmark problem numerical results illustrate the proposed algorithm’s effectiveness and competitiveness relative to other three-term algorithms. Additionally, the algorithm is extended to effectively address the image denoising problem.

Keywords: nonlinear monotone equations; conjugate gradient method; convergence analysis; image denoising (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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