gradient method
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2022 ◽  
Vol 173 ◽  
pp. 222-238
Author(s):  
O. Benchettou ◽  
A.H. Bentbib ◽  
A. Bouhamidi ◽  
K. Kreit

Author(s):  
Mezher M. Abed ◽  
Ufuk Öztürk ◽  
Hisham M. Khudhur

The nonlinear conjugate gradient method is an effective technique for solving large-scale minimizations problems, and has a wide range of applications in various fields, such as mathematics, chemistry, physics, engineering and medicine. This study presents a novel spectral conjugate gradient algorithm (non-linear conjugate gradient algorithm), which is derived based on the Hisham–Khalil (KH) and Newton algorithms. Based on pure conjugacy condition The importance of this research lies in finding an appropriate method to solve all types of linear and non-linear fuzzy equations because the Buckley and Qu method is ineffective in solving fuzzy equations. Moreover, the conjugate gradient method does not need a Hessian matrix (second partial derivatives of functions) in the solution. The descent property of the proposed method is shown provided that the step size at meets the strong Wolfe conditions. In numerous circumstances, numerical results demonstrate that the proposed technique is more efficient than the Fletcher–Reeves and KH algorithms in solving fuzzy nonlinear equations.


2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Zabidin Salleh ◽  
Adel Almarashi ◽  
Ahmad Alhawarat

AbstractThe conjugate gradient method can be applied in many fields, such as neural networks, image restoration, machine learning, deep learning, and many others. Polak–Ribiere–Polyak and Hestenses–Stiefel conjugate gradient methods are considered as the most efficient methods to solve nonlinear optimization problems. However, both methods cannot satisfy the descent property or global convergence property for general nonlinear functions. In this paper, we present two new modifications of the PRP method with restart conditions. The proposed conjugate gradient methods satisfy the global convergence property and descent property for general nonlinear functions. The numerical results show that the new modifications are more efficient than recent CG methods in terms of number of iterations, number of function evaluations, number of gradient evaluations, and CPU time.


2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Ibrahim Mohammed Sulaiman ◽  
Maulana Malik ◽  
Aliyu Muhammed Awwal ◽  
Poom Kumam ◽  
Mustafa Mamat ◽  
...  

AbstractThe three-term conjugate gradient (CG) algorithms are among the efficient variants of CG algorithms for solving optimization models. This is due to their simplicity and low memory requirements. On the other hand, the regression model is one of the statistical relationship models whose solution is obtained using one of the least square methods including the CG-like method. In this paper, we present a modification of a three-term conjugate gradient method for unconstrained optimization models and further establish the global convergence under inexact line search. The proposed method was extended to formulate a regression model for the novel coronavirus (COVID-19). The study considers the globally infected cases from January to October 2020 in parameterizing the model. Preliminary results have shown that the proposed method is promising and produces efficient regression model for COVID-19 pandemic. Also, the method was extended to solve a motion control problem involving a two-joint planar robot.


Author(s):  
Nan Meng ◽  
Yun-Bin Zhao

AbstractSparse signals can be possibly reconstructed by an algorithm which merges a traditional nonlinear optimization method and a certain thresholding technique. Different from existing thresholding methods, a novel thresholding technique referred to as the optimal k-thresholding was recently proposed by Zhao (SIAM J Optim 30(1):31–55, 2020). This technique simultaneously performs the minimization of an error metric for the problem and thresholding of the iterates generated by the classic gradient method. In this paper, we propose the so-called Newton-type optimal k-thresholding (NTOT) algorithm which is motivated by the appreciable performance of both Newton-type methods and the optimal k-thresholding technique for signal recovery. The guaranteed performance (including convergence) of the proposed algorithms is shown in terms of suitable choices of the algorithmic parameters and the restricted isometry property (RIP) of the sensing matrix which has been widely used in the analysis of compressive sensing algorithms. The simulation results based on synthetic signals indicate that the proposed algorithms are stable and efficient for signal recovery.


2022 ◽  
Vol 355 ◽  
pp. 03005
Author(s):  
Yunhong Wang ◽  
Dan Liu

Blind image deblurring is a long-standing challenging problem to improve the sharpness of an image as a prerequisite step. Many iterative methods are widely used for the deblurring image, but care must be taken to ensure that the methods have fast convergence and accuracy solutions. To address these problems, we propose a gradient-wise step size search strategy for iterative methods to achieve robustness and accelerate the deblurring process. We further modify the conjugate gradient method with the proposed strategy to solve the bling image deblurring problem. The gradient-wise step size aims to update gradient for each pixel individually, instead of updating step size by the fixed factor. The modified conjugate gradient method improves the convergence performance computation speed with a gradient-wise step size. Experimental results show that our method effectively estimates the sharp image for both motion blur images and defocused images. The results of synthetic datasets and natural images are better than what is achieved with other state-of-the-art blind image deblurring methods.


2022 ◽  
pp. 111739
Author(s):  
Siyuan Wu ◽  
Zhe Huang ◽  
Baishan Chen ◽  
Xiao Liu ◽  
Yunzhu Ma ◽  
...  

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2450
Author(s):  
Jun Huo ◽  
Yuping Wu ◽  
Guoen Xia ◽  
Shengwei Yao

In this paper, a new subspace gradient method is proposed in which the search direction is determined by solving an approximate quadratic model in which a simple symmetric matrix is used to estimate the Hessian matrix in a three-dimensional subspace. The obtained algorithm has the ability to automatically adjust the search direction according to the feedback from experiments. Under some mild assumptions, we use the generalized line search with non-monotonicity to obtain remarkable results, which not only establishes the global convergence of the algorithm for general functions, but also R-linear convergence for uniformly convex functions is further proved. The numerical performance for both the traditional test functions and image restoration problems show that the proposed algorithm is efficient.


Author(s):  
Иван Петрович Добролюбов ◽  
Олег Федорович Савченко ◽  
Виктор Валентинович Альт ◽  
Олег Владимирович Ёлкин ◽  
Денис Николаевич Клименко

Рассмотрены вопросы уменьшения погрешности идентификации технического состояния двигателя внутреннего сгорания и его составных частей как объекта экспертизы путем настраивания параметров применяемой в измерительной экспертной системе виртуальной модели ДВС. Для настройки модели предложено применение градиентного метода, обеспечивающего наиболее быструю минимизацию погрешности идентификации Purpose and methods. Improving the accuracy of identification for the technical condition of the internal combustion engine (ICE) in operational conditions using the engine measurement expert system (EMSE) is addressed by adjusting the computer dynamic model of the internal combustion engine. Results. Algorithmic schemes of computer models for the state of the ICE are obtained using the equations of its dynamics, which takes into account the factors such as the movement of the fuel supply body, the force on the hook - the load. The structural schemes of modeling at the input of a step-by-step action are presented. A promising method of tuning the model in the EMSE is proposed, which consists of measuring its working processes, in particular the angular acceleration of the crankshaft, for a specific brand of ICE. Then the corresponding set of models of its technical condition is obtained: normal, permissible, limit, pre-accident and emergency. By adjusting the values of the coefficients of these models in the EMSE, they achieve their coincidence with the actual state of the ICE. The identification error is minimized using the gradient method of steepest descent. The presence of several computer models is a practical advantage in the examination of the technical condition of the tested engines allowing its effective implementation in operational conditions. In this case, based on the experience of operation, the computer model closest to the actual state of the ICE is adjusted. At the same time, the efficiency of localization of ICE malfunctions increases, since the coefficients reflecting the state of the engine components and systems are consistently adjusted. Conclusions. The application of the proposed methodology using the criterion of minimizing the identification error by the gradient method allows implementation of this effective method for identifying the state of the ICE. It increases the reliability of determining the technical state of the ICE and its components by adjusting the computer model


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