M. Malik, I. Sulaiman, A. Abubakar, Gianinna Ardaneswari, Sukono
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引用次数: 9
摘要
共轭梯度法(CG)是一种优化方法,在应用中收敛速度快。到目前为止,已经开发了许多CG方法来提高计算性能,并已应用于现实世界的问题。本文提出了一种新的求解无约束优化问题的混合三项CG方法。搜索方向是Hestenes-Stiefel (HS)和polak - ribi - polyak (PRP) CG系数的三项混合形式,满足充分下降条件。此外,还证明了该方法在弱Wolfe线搜索下的全局收敛性。通过几个测试函数,数值结果表明,与现有的一些方法相比,所提出的方法是最有效的。此外,该方法还用于图像恢复和组合选择等实际应用问题。
A new family of hybrid three-term conjugate gradient method for unconstrained optimization with application to image restoration and portfolio selection
The conjugate gradient (CG) method is an optimization method, which, in its application, has a fast convergence. Until now, many CG methods have been developed to improve computational performance and have been applied to real-world problems. In this paper, a new hybrid three-term CG method is proposed for solving unconstrained optimization problems. The search direction is a three-term hybrid form of the Hestenes-Stiefel (HS) and the Polak-Ribiére-Polyak (PRP) CG coefficients, and it satisfies the sufficient descent condition. In addition, the global convergence properties of the proposed method will also be proved under the weak Wolfe line search. By using several test functions, numerical results show that the proposed method is most efficient compared to some of the existing methods. In addition, the proposed method is used in practical application problems for image restoration and portfolio selection.
期刊介绍:
AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.