This paper introduces two three-term trust region conjugate gradient algorithms, TT-TR-WP and TT-TR-CG, which are capable of converging under non-Lipschitz continuous gradient functions without any additional conditions. These algorithms possess sufficient descent and trust region properties, and demonstrate global convergence. In order to assess their numerical performance, we compare them with two classical algorithms in terms of restoring noisy gray-scale and color images as well as solving large-scale unconstrained problems.
View Article and Find Full Text PDFFor large-scale unconstrained optimization problems and nonlinear equations, we propose a new three-term conjugate gradient algorithm under the Yuan-Wei-Lu line search technique. It combines the steepest descent method with the famous conjugate gradient algorithm, which utilizes both the relevant function trait and the current point feature. It possesses the following properties: (i) the search direction has a sufficient descent feature and a trust region trait, and (ii) the proposed algorithm globally converges.
View Article and Find Full Text PDFIn this paper, a modified BFGS algorithm is proposed for unconstrained optimization. The proposed algorithm has the following properties: (i) a nonmonotone line search technique is used to obtain the step size [Formula: see text] to improve the effectiveness of the algorithm; (ii) the algorithm possesses not only global convergence but also superlinear convergence for generally convex functions; (iii) the algorithm produces better numerical results than those of the normal BFGS method.
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