Displaying similar documents to “Open problems in nonlinear conjugate gradient algorithms for unconstrained optimization.”

A modified Fletcher-Reeves conjugate gradient method for unconstrained optimization with applications in image restoration

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...

A self-scaling memoryless BFGS based conjugate gradient method using multi-step secant condition for unconstrained minimization

Yongjin Kim, Yunchol Jong, Yong Kim (2024)

Applications of Mathematics

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Conjugate gradient methods are widely used for solving large-scale unconstrained optimization problems, because they do not need the storage of matrices. Based on the self-scaling memoryless Broyden-Fletcher-Goldfarb-Shanno (SSML-BFGS) method, new conjugate gradient algorithms CG-DESCENT and CGOPT have been proposed by W. Hager, H. Zhang (2005) and Y. Dai, C. Kou (2013), respectively. It is noted that the two conjugate gradient methods perform more efficiently than the SSML-BFGS method....

Adjustment of the scaling parameter of Dai-Kou type conjugate gradient methods with application to motion control

Mahbube Akbari, Saeed Nezhadhosein, Aghile Heydari (2024)

Applications of Mathematics

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We introduce a new scaling parameter for the Dai-Kou family of conjugate gradient algorithms (2013), which is one of the most numerically efficient methods for unconstrained optimization. The suggested parameter is based on eigenvalue analysis of the search direction matrix and minimizing the measure function defined by Dennis and Wolkowicz (1993). The corresponding search direction of conjugate gradient method has the sufficient descent property and the extended conjugacy condition....

A new nonmonotone adaptive trust region algorithm

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...