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12 results for “Conjugate Gradient Method”
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Research ArticleOpen accessPhrase in the titleA Developed Version of Conjugate Gradient Method With a New Parameter for Dai-Liao Conjugacy Condition With an Application to Solar PanelAhmad Alhawarat, Ramadan Sabra, Mehiddin Al-Baali et al.Conjugate Gradient (CG) methods are broadly employed in solving bigger-scale unconstrained optimization problems. Two famous methods are the Hestenes–Stiefel (HS) as well as Polak–Ribière–Polyak (PRP) CG methods, which usually work well in practice. However, they cannot satisfy the Global Convergence (GC) property. To retain and enhance the previous practical behavior as well as rectify the latter difficulty, this paper constructs … …Journal of Computer Science, Vol. 21, Issue 7 · 15 Jul 2025 · 3,147 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleSufficient Descent Condition of the Polak-Ribière-Polyak (PRP) Conjugate Gradient Method without Line SearchAbdelrahman A., KH. I. Osman, Osman O.O. Yousif et al.Nonlinear conjugate gradient methods for unconstrained optimization problems are used in many aspects of theoretical and applied sciences. They are iterative methods, so at any iteration a step length is computed using a method called line search. In most cases, the sufficient descent condition plays an important role to prove the global convergence of a conjugate gradient method. Due to … …Journal of Mathematics and Statistics, Vol. 18, Issue 1 · 14 Mar 2022 · 6,360 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleA Robust Modification of Hestenes–Stiefel Conjugate Gradient Method with Strong Wolfe Line SearchAwad Abdelrahman, Osman O.O. Yousif, Khalid I. OsmanNonlinear Conjugate Gradient (CG) methods are extensively used for solving large-scale unconstrained optimization problems. Numerous of studies constructed scales and modifications have been conducted recently to improve (CG) methods. In this paper, a simple modified by its conjugate gradient method was proposed. In addition to, established global convergence property and sufficient descent condition, under Strong Wolfe line search. Numerical result … …Journal of Mathematics and Statistics, Vol. 16, Issue 1 · 14 May 2020 · 6,743 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleA New Spectral Conjugate Gradient Method for Nonlinear Unconstrained OptimizationIbtisam A. Masmali, Zabidin Salleh, Ahmad AlhawaratTheconjugate gradient method is widely used to solve large scale unconstrainedoptimization problems. However, the rate of convergence conjugate gradient method is linearunless it restarted. In this study, we present a new spectral conjugategradient modification formula with restart property obtains the globalconvergence and descent properties.In addition, we proposed a new restart condition for Fletcher-Reeves conjugate gradient formula. The numerical resultsdemonstrated that … …Journal of Computer Science, Vol. 17, Issue 6 · 5 Jul 2021 · 6,653 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleInclusion Identification by Inverse Application of Boundary Element Method, Genetic Algorithm and Conjugate Gradient MethodMahmud Khodadad, Mohsen Dashti ArdakaniCharacterization of the interior of an inhomogeneous body using displacement measurements obtained by conducting a simple tension test was investigated. A homogeneous elastic solid body is assumed to have another solid body with arbitrary shape hidden inside it. The shape and physical properties of this inclusion were unknown. The Boundary Element Method (BEM) coupled with a mete heuristic Genetic Algorithm … …American Journal of Applied Sciences, Vol. 5, Issue 9 · 30 Sep 2008 · 6,758 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleConjugate Gradient ‎Method: A Developed Version to Resolve Unconstrained Optimization ProblemsAhmad Alhawarat, Nguyen-Thoi Trung, Zabidin SallehOne of the important methods that are widely utilized to resolve ‎unconstrained ‎optimization problems is the Conjugate Gradient (CG) method. This paper aims to propose a new version of the CG method on the basis of Weak Wolfe-Powell (WWP) line search. The assumption is bounded below optimization problems with the Lipschitz continuous gradient. The new parameter obtains global convergence properties … …Journal of Computer Science, Vol. 16, Issue 9 · 18 Sep 2020 · 6,887 accessesView PDFCite
Research ArticleOpen accessIn the keywordsDiscretized Scheme Examining Convergence and Geometric Ratio Profiles for Control Problem Constrained by Evolution EquationO. OlotuProblem statement: Here, we develop a discretized scheme using only the penalty method without involving the multiplier parameter to examine the convergence and geometric ratio profiles. Approach: This approach reduces computational time arising from less data manipulation. Objectively, we wish to obtain a numerical solution comparing favourably with the analytic solution.. Methodologically, we discretize the given problem, obtain an unconstrained … …Journal of Mathematics and Statistics, Vol. 7, Issue 2 · 18 May 2011 · 7,370 accessesView PDFCite
Research ArticleOpen accessIn the abstractA Robust Recognition System for Pecan Weevil using Artificial Neural NetworksSaleh Mufleh Al-SaqerProblem statement: Pecan Weevil is a widely found pest among pecan trees and these pests are known to cause significant damage to the pecan trees resulting in enormous annual losses to pecan growers. Traditional identification techniques for pecan weevil include traps with pheromones to detect the infestation of these pests. However, these traditional methods require expensive labor hours to set-up … …American Journal of Applied Sciences, Vol. 9, Issue 9 · 14 Jul 2012 · 6,831 accessesView PDFCite
Research ArticleOpen accessIn the abstractQuadratic Convergence Ratio of Constrained Optimal Control ProblemsO. OlotuProblem statement: Earlier Researchers developed algorithms for solving quadratic control problems, but did not address the quadratic convergence ratio profile. Approach: Hence, the objective of this work is using our developed scheme, Discretized Continuous Algorithm (DCA), to examine both convergence profile and quadratic ratio profile demonstrating the effectiveness and efficiency of the scheme. Methodologically, we obtained generalized unconstrained formulation of … …Journal of Mathematics and Statistics, Vol. 6, Issue 1 · 31 Mar 2010 · 7,372 accessesView PDFCite
Research ArticleOpen accessIn the abstractImbedding the Multiplier in a Discretized Optimal Control Problem With Real Coefficients Via the Penalty and Multiplier MethodsO. OlotuProblem statement: Many earlier schemes, particularly the Function Space Algorithm (FSA) which sidetracks the knowledge of operator, for solving quadratic optimal control problems have been computationally involving and iteratively high. Approach: Though, some of these earlier schemes developed operators consisting of complicated integrals still very difficult to evaluate. Here, objectively, a new scheme, Discretized Continuous Algorithm (DCA), is proposed with … …Journal of Mathematics and Statistics, Vol. 6, Issue 1 · 31 Mar 2010 · 7,041 accessesView PDFCite