Two classes of spectral three-term derivative-free method for solving nonlinear equations with application

Ibrahim, Abdulkarim Hassan; Alshahrani, Mohammed; Al-Homidan, Suliman

doi:10.1007/s11075-023-01679-7

Cited by 5 publications

(1 citation statement)

References 53 publications

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“…Waziri et al [21] proposed two DY-type iterative methods for solving (1). By using the projection method [10], Abdulkarim et al [22] introduced two classes of three-term methods for solving (1) and established the global convergence under a weaker monotonicity condition.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Subspace Minimization Conjugate Gradient Method for Solving Nonlinear Monotone Equations with Convex Constraints

Song,

Liu

2024

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The subspace minimization conjugate gradient (SMCG) methods proposed by Yuan and Store are efficient iterative methods for unconstrained optimization, where the search directions are generated by minimizing the quadratic approximate models of the objective function at the current iterative point. Although the SMCG methods have illustrated excellent numerical performance, they are only used to solve unconstrained optimization problems at present. In this paper, we extend the SMCG methods and present an efficient SMCG method for solving nonlinear monotone equations with convex constraints by combining it with the projection technique, where the search direction is sufficiently descent.Under mild conditions, we establish the global convergence and R-linear convergence rate of the proposed method. The numerical experiment indicates that the proposed method is very promising.

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