2019
DOI: 10.3846/mma.2019.033
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A New Three-Term Conjugate Gradient-Based Projection Method for Solving Large-Scale Nonlinear Monotone Equations

Abstract: A new three-term conjugate gradient-based projection method is presented in this paper for solving large-scale nonlinear monotone equations. This method is derivative-free and it is suitable for solving large-scale nonlinear monotone equations due to its lower storage requirements. The method satisfies the sufficient descent condition FTkdk ≤ −τ‖Fk‖2, where τ > 0 is a constant, and its global convergence is also established. Numerical results show that the method is efficient and promising.

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Cited by 10 publications
(6 citation statements)
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“…The inequality (24) implies that { v (t) −ṽ } t≥0 is nonincreasing and therefore, {v (t) } t≥0 is bounded. That is,…”
Section: Convergence Analysismentioning
confidence: 99%
See 2 more Smart Citations
“…The inequality (24) implies that { v (t) −ṽ } t≥0 is nonincreasing and therefore, {v (t) } t≥0 is bounded. That is,…”
Section: Convergence Analysismentioning
confidence: 99%
“…In this section, the numerical behavior of the proposed algorithm (Algorithm 1) in comparison with two existing methods is examined. We compare the performance of Algorithm 1 with a conjugate gradient projection method for solving nonlinear equations with convex constraints by Zheng et al [46] denoted as Algorithm 2 and a new three-term conjugate gradient-based projection method for solving large-scale nonlinear monotone equations by Koorapetse et al [24] denoted as Algorithm 3. Algorithm 1 is implemented using the following parameters: σ = 0.001, µ = 1 ρ = 0.7, γ = 1.7 and λ = 1.2.…”
Section: Numerical Experimentsmentioning
confidence: 99%
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“…Gao and He [25] chose a part of the Liu-Storey (LS) conjugate parameter as a new conjugate parameter and further proposed a three-term conjugate gradient (TTCG) method for solving nonlinear monotone equations with convex constraints. Motivated by the modified Dai-Yuan (DY) method [26], Koorapetse and Kaelo [27] proposed a new three-term conjugate gradient-based projection method to solve nonlinear monotone equations with convex constraints. The common feature of these methods is that they are stable in descent property and convergence, and the computing performance is satisfactory.…”
Section: Introductionmentioning
confidence: 99%
“…The DY conjugate gradient method [28] is one of the most famous conjugate gradient methods for solving unconstrained optimization problems, which is known for the stability. In order to establish the stable and effective method for solving monotone nonlinear equations with convex constraints, in this paper we propose a three-term derivativefree projection method based on the structures of the methods [25,27] and the DY conjugate gradient method [28]. This method inherits the stability of the DY method, and greatly improves its computing performance.…”
Section: Introductionmentioning
confidence: 99%