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Modified Three-Term Liu–Storey Conjugate Gradient Method for Solving Unconstrained Optimization Problems and Image Restoration Problems
Mathematical Problems in Engineering ( IF 1.430 ) Pub Date : 2020-10-19 , DOI: 10.1155/2020/7859286
Yulun Wu 1 , Mengxiang Zhang 1 , Yan Li 2
Affiliation  

A new three-term conjugate gradient method is proposed in this article. The new method was able to solve unconstrained optimization problems, image restoration problems, and compressed sensing problems. The method is the convex combination of the steepest descent method and the classical LS method. Without any linear search, the new method has sufficient descent property and trust region property. Unlike previous methods, the information for the function is assigned to . Next, we make some reasonable assumptions and establish the global convergence of this method under the condition of using the modified Armijo line search. The results of subsequent numerical experiments prove that the new algorithm is more competitive than other algorithms and has a good application prospect.

中文翻译:

求解无约束优化问题和图像恢复问题的改进三项刘层共轭梯度法

本文提出了一种新的三项共轭梯度法。新方法能够解决不受约束的优化问题,图像恢复问题和压缩感测问题。该方法是最速下降法和经典LS法的凸组合。在没有任何线性搜索的情况下,新方法具有足够的下降特性和信任区域特性。与以前的方法不同,该功能的信息分配给接下来,我们做出一些合理的假设,并在使用改进的Armijo线搜索的条件下建立该方​​法的全局收敛性。后续数值实验结果表明,该新算法比其他算法更具竞争力,具有良好的应用前景。
更新日期:2020-10-19
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