A conjugate gradient method for unconstrained optimization problems.
Yuan, Gonglin (2009)
International Journal of Mathematics and Mathematical Sciences
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Yuan, Gonglin (2009)
International Journal of Mathematics and Mathematical Sciences
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Zhang, Ming-Liang, Xiao, Yun-Hai, Zhou, Dangzhen (2010)
Mathematical Problems in Engineering
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Zhang, Jianguo, Xiao, Yunhai, Wei, Zengxin (2009)
Mathematical Problems in Engineering
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Zainab Hassan Ahmed, Mohamed Hbaib, Khalil K. Abbo (2024)
Applications of Mathematics
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The Fletcher-Reeves (FR) method is widely recognized for its drawbacks, such as generating unfavorable directions and taking small steps, which can lead to subsequent poor directions and steps. To address this issue, we propose a modification to the FR method, and then we develop it into the three-term conjugate gradient method in this paper. The suggested methods, named ``HZF'' and ``THZF'', preserve the descent property of the FR method while mitigating the drawbacks. The algorithms...
Andrei, Neculai (2011)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Hoai An Le Thi, Mohand Ouanes (2006)
RAIRO - Operations Research
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The purpose of this paper is to demonstrate that, for globally minimize one dimensional nonconvex problems with both twice differentiable function and constraint, we can propose an efficient algorithm based on Branch and Bound techniques. The method is first displayed in the simple case with an interval constraint. The extension is displayed afterwards to the general case with an additional nonconvex twice differentiable constraint. A quadratic bounding function which is better than...
Zhensheng Yu, Qiang Li (2009)
Applications of Mathematics
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By using some NCP functions, we reformulate the extended linear complementarity problem as a nonsmooth equation. Then we propose a self-adaptive trust region algorithm for solving this nonsmooth equation. The novelty of this method is that the trust region radius is controlled by the objective function value which can be adjusted automatically according to the algorithm. The global convergence is obtained under mild conditions and the local superlinear convergence rate is also established...
Ahmad Kamandi, Keyvan Amini (2022)
Applications of Mathematics
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We propose a new and efficient nonmonotone adaptive trust region algorithm to solve unconstrained optimization problems. This algorithm incorporates two novelties: it benefits from a radius dependent shrinkage parameter for adjusting the trust region radius that avoids undesirable directions and exploits a new strategy to prevent sudden increments of objective function values in nonmonotone trust region techniques. Global convergence of this algorithm is investigated under some mild...
Nada I. Đuranović-Miličić (2005)
The Yugoslav Journal of Operations Research
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Nada I. Đuranović-Miličić (2008)
The Yugoslav Journal of Operations Research
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Cheng, Wanyou, Zhang, Zongguo (2009)
Mathematical Problems in Engineering
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