Spectral CG Algorithm for Solving Fuzzy Nonlinear Equations

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.

Two efficient modifications of AZPRP conjugate gradient method with sufficient descent property

The 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.

On three-term conjugate gradient method for optimization problems with applications on COVID-19 model and robotic motion control

The 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.

Gradient-wise search strategy for blind image deblurring

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.

Motion control of the two joint planar robotic manipulators through accelerated Dai–Liao method for solving system of nonlinear equations

PurposeThe purpose of this research is to propose a new choice of nonnegative parameter t in Dai–Liao conjugate gradient method.Design/methodology/approachConjugate gradient algorithms are used to solve both constrained monotone and general systems of nonlinear equations. This is made possible by combining the conjugate gradient method with the Newton method approach via acceleration parameter in order to present a derivative-free method.FindingsA conjugate gradient method is presented by proposing a new Dai–Liao nonnegative parameter. Furthermore the proposed method is successfully applied to handle the application in motion control of the two joint planar robotic manipulators.Originality/valueThe proposed algorithm is a new approach that will not either submitted or publish somewhere.

Numerical Optimization of the β-Type Stirling Engine Performance Using the Variable-Step Simplified Conjugate Gradient Method

This study focuses on optimizing a 100-W-class β-Type Stirling engine by combining the modified thermodynamic model and the variable-step simplified conjugate gradient (VSCGM) method. For the modified thermodynamic model, non-uniform pressure is directly introduced into the energy equation, so the indicated power and heat transfer rates can reach energy balance while the VSCGM is an updated version of the simplified conjugate gradient method (SCGM) with adaptive increments and step lengths to the optimization process; thus, it requires fewer iterations to reach the optimal solution than the SCGM. For the baseline case, the indicated power progressively raises from 88.2 to 210.2 W and the thermal efficiency increases from 34.8 to 46.4% before and after optimization, respectively. The study shows the VSCGM possesses robust property. All optimal results from the VSCGM are well-matched with those of the computational fluid dynamics (CFD) model. Heating temperature and rotation speed have positive effects on optimal engine performance. The optimal indicated power rises linearly with the charged pressure, whereas the optimal thermal efficiency tends to decrease. The study also points out that results of the modified thermodynamic model with fixed values of unknowns agree well with the CFD results at points far from the baseline case.

Estimation of local heat flux for turbulent flow in a helical coil tube by conjugate gradient method

Estimation of local heat flux is challenging in a helical coil tube heat exchanger due to the complex flow field developed by tube curvature. The heat flux has uneven distribution in the angular direction of the tube cross-section. The current research aims to estimate the local heat flux at the fluid-solid interface for the turbulent flow of water in a helical coil tube by solving the inverse heat conduction problem (IHCP). Conjugate gradient method (CGM) with an adjoint problem is used as an inverse algorithm. First, the commercial CFD software ANSYS FLUENT is used for solving the governing equations of continuity, momentum, and energy for turbulent flow to obtain the heat flux at the fluid-solid interface. This heat flux is used to determine the temperature distribution at the outer surface of the tube. The heat flux is then considered unknown and it is estimated by CGM algorithm with the developed in-house code in MATLAB. The result shows that the estimation of heat flux by CGM is very accurate.