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In this note, we show that the proof of Remark 3 of Lemma 3.2 in “A three-term derivative-free projection method for nonlinear monotone system of equations” (Calcolo 53:427–450, 2016) is not correct, which implies that the conclusion of Remark 3 is not appropriate to prove Theorem 3.1. A new proof of Remark 3 is established, which guarantees the corresponding global convergence Theorem 3.1. Throughout,...
In this paper, a self-adaptive three-term conjugate gradient method is proposed for solving monotone nonlinear equations with convex constraints. Under milder conditions, the global convergence of the method is proved. Numerical experiments reported in this paper illustrate that the method is stable and efficient for monotone nonlinear equations, especially for the large-scale problems with convex...
In this paper, we propose a three-term conjugate gradient method, which has two attractive properties that the search direction is descent and satisfies the famous D-L conjugacy condition without any line search. Moreover, this new three-term conjugate gradient method can be viewed as a modification of the memoryless BFGS method. By combining this new three-term conjugate gradient method with the...
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