An efficient modified PRP-FR hybrid conjugate gradient method for solving unconstrained optimization problems

Mtagulwa, Peter; Kaelo, P.

doi:10.1016/j.apnum.2019.06.003

Cited by 23 publications

(8 citation statements)

References 19 publications

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“…In Ref. 18 , authors proposed a hybrid conjugate gradient algorithm combining PRP and FR algorithms. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Some convergently three-term trust region conjugate gradient algorithms under gradient function non-Lipschitz continuity

Hu,

Wu,

Yuan

2024

Sci Rep

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This paper introduces two three-term trust region conjugate gradient algorithms, TT-TR-WP and TT-TR-CG, which are capable of converging under non-Lipschitz continuous gradient functions without any additional conditions. These algorithms possess sufficient descent and trust region properties, and demonstrate global convergence. In order to assess their numerical performance, we compare them with two classical algorithms in terms of restoring noisy gray-scale and color images as well as solving large-scale unconstrained problems. In restoring noisy gray-scale images, we set the performance of TT-TR-WP as the standard, then TT-TR-CG takes around 2.33 times longer. The other algorithms around 2.46 and 2.41 times longer, respectively. In solving the same color images, the proposed algorithms exhibit relative good performance over other algorithms. Additionally, TT-TR-WP and TT-TR-CG are competitive in unconstrained problems, and the former has wide applicability while the latter has strong robustness. Moreover, the proposed algorithms are both more outstanding than the baseline algorithms in terms of applicability and robustness.

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“…In Ref. 18 , authors proposed a hybrid conjugate gradient algorithm combining PRP and FR algorithms. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Some convergently three-term trust region conjugate gradient algorithms under gradient function non-Lipschitz continuity

Hu,

Wu,

Yuan

2024

Sci Rep

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“…Other CG algorithms (Cao and Wu, 2020;Joo et al, 1997), for this purpose, were also brought in the literature. In addition to them, some improved CG methods such as those of (Mtagulwa and Kaelo, 2019;Jiang and Jian, 2019;Wang et al, 2018;Fatemi, 2016) were presented for general optimization problems.…”

Section: Introductionmentioning

confidence: 99%

Geometri Uydurma için En İyi Eşlenik Gradyan Yönteminin Tespit Edilmesi

Kiran

2022

Konya Journal of Engineering Sciences

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In this study, it is aimed to determine the optimal conjugate gradient (CG) method for the geometry fitting of 2D measured profiles. To this end, the three well-known CG methods such as the Fletcher-Reeves, Polak-Ribiere and Hestenes-Stiefel were employed. For testing those methods performances, the five primitive geometries accommodating circle, square, triangle, ellipse and rectangle were first built with a 3D printer, and then they were scanned with a coordinate measuring machine (CMM) to achieve their 2D profiles. The nonlinear least squares procedure was implemented to minimize the error between those measured data and modeled ones. An iterative line search was utilized for this task. The search direction was calculated using the above-mentioned CG methods. During the geometry fitting process, the number of function evaluations at each iteration were computed and the total number of function evaluations were set to be a performance measure of the CG method in question when it converged. By using these performance measures, the performance and data profiles were created to efficiently determine the optimal CG method. Based on performance profiles, it can be stated that the Fletcher-Reeves and Polak-Ribiere methods are the fastest ones on three test geometries out of five. In addition to that, all the CG methods were able to complete the geometry fitting of 80% of test geometries. On the other hand, by examining the data profiles, it was determined that the Polak-Ribiere and Hestenes-Stiefel methods achieve their maximum capabilities of the completing geometry fitting (i.e., 80%) with much lower number of function evaluations than the Fletcher-Reeves method. Besides, in most geometries, the Polak-Ribiere method outperformed the others, thereby it was determined to be the optimal one for the geometry fitting. As a conclusion, the reported results in this work might help the end-users who study on the CMM data processing to conduct an efficient geometry fitting.

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“…Therefore, many conjugant gradient line-search methods are suggested; see, for example, refs. [18,[24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

A Family of Hybrid Stochastic Conjugate Gradient Algorithms for Local and Global Minimization Problems

et al. 2022

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This paper contains two main parts, Part I and Part II, which discuss the local and global minimization problems, respectively. In Part I, a fresh conjugate gradient (CG) technique is suggested and then combined with a line-search technique to obtain a globally convergent algorithm. The finite difference approximations approach is used to compute the approximate values of the first derivative of the function f. The convergence analysis of the suggested method is established. The comparisons between the performance of the new CG method and the performance of four other CG methods demonstrate that the proposed CG method is promising and competitive for finding a local optimum point. In Part II, three formulas are designed by which a group of solutions are generated. This set of random formulas is hybridized with the globally convergent CG algorithm to obtain a hybrid stochastic conjugate gradient algorithm denoted by HSSZH. The HSSZH algorithm finds the approximate value of the global solution of a global optimization problem. Five combined stochastic conjugate gradient algorithms are constructed. The performance profiles are used to assess and compare the rendition of the family of hybrid stochastic conjugate gradient algorithms. The comparison results between our proposed HSSZH algorithm and four other hybrid stochastic conjugate gradient techniques demonstrate that the suggested HSSZH method is competitive with, and in all cases superior to, the four algorithms in terms of the efficiency, reliability and effectiveness to find the approximate solution of the global optimization problem that contains a non-convex function.

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An efficient modified PRP-FR hybrid conjugate gradient method for solving unconstrained optimization problems

Cited by 23 publications

References 19 publications

Some convergently three-term trust region conjugate gradient algorithms under gradient function non-Lipschitz continuity

Some convergently three-term trust region conjugate gradient algorithms under gradient function non-Lipschitz continuity

Geometri Uydurma için En İyi Eşlenik Gradyan Yönteminin Tespit Edilmesi

A Family of Hybrid Stochastic Conjugate Gradient Algorithms for Local and Global Minimization Problems

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