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Taking advantage of the attractive features of Hestenes-Stiefel and Dai-Yuan conjugate gradient methods, we suggest two globally convergent hybridizations of these methods following Andrei's approach of hybridizing the conjugate gradient parameters convexly and Powell's approach of nonnegative restriction of the conjugate gradient parameters. In our methods, the hybridization parameter is obtained based on a recently proposed hybrid secant equation. Numerical results demonstrating the efficiency of the proposed methods are reported  

Based on a modified secant equation proposed by Li and Fukushima, we derive a stepsize for the Barzilai-Borwein gradient method. Then, using the newly proposed stepsize and another effective stepsize proposed by Dai et al. in an adaptive scheme that is based on the objective function convexity, we suggest a modified two-point stepsize gradient algorithm. We also show that the limit point of the sequence generated by our algorithm is first-order critical. Finally, our numerical comparisons done on a set of unconstrained optimization test problems from the CUTEr collection are presented. At first, we compare the performance of our algorithm with two other two-point stepsize gradient algorithms... 

Following the approach proposed by Dai and Liao, we introduce two nonlinear conjugate gradient methods for unconstrained optimization problems. One of our proposed methods is based on a modified version of the secant equation proposed by Zhang, Deng and Chen, and Zhang and Xu, and the other is based on the modified BFGS update proposed by Yuan. An interesting feature of our methods is their account of both the gradient and function values. Under proper conditions, we show that one of the proposed methods is globally convergent for general functions and that the other is globally convergent for uniformly convex functions. To enhance the performance of the line search procedure, we also... 

In this paper, we propose a new derivative-free preconditioned conjugate gradient method in order for solving large-scale square and under-determined nonlinear systems of equations. The proposed method is also equipped with a relaxed nonmonotone line search technique. Under some suitable assumptions, the global convergence property is established. Numerical results on some square and under-determined test systems show the efficiency and effectiveness of the new method in practice. An application of the new method for solving nonlinear integro-differential equations is also provided. © 2016 Elsevier Ltd  

The aim of this study is to develop iterative regularization algorithms based on parameter and function estimation techniques to solve two-dimensional/axisymmetric transient inverse heat conduction problems in curvilinear coordinate system. The multiblock method is used for geometric decomposition of the physical domain into regions with patched-overlapped interface grids. The central finite-difference version of the alternating-direction implicit technique together with structured body-fitted grids is implemented for numerical solution of the direct problem and other partial differential equations derived by inverse analysis. The approach of estimating unknown parameters and functions is... 

We propose an algorithm based on mutual information to address the problem of online reconstruction of dynamic MRI from partial k-space measurements. Most of previous compressed sensing (CS) based methods successfully leverage sparsity constraint for offline reconstruction of MR images, yet they are not used in online applications due to their complexities. In this paper, we formulate the reconstruction as a constraint optimization problem and try to maximize the mutual information between the current and the previous time frames. Conjugate gradient method is used to solve the optimization problem. Using Cartesian mask to undersample k-space measurements, the proposed method reduces... 

The objective of this article is to study gas temperature estimation in a partially filled rotating cylinder. From the measured temperatures on the shell, an inverse analysis is presented for estimating the gas temperature in an arbitrary cross-section of the aforementioned system. A finite-volume method is employed to solve the direct problem. By minimizing the objective function, a hybrid effective algorithm, which contains a local optimization algorithm, is adopted to estimate the unknown parameter. The measured data are simulated by adding random errors to the exact solution. The effects of measurement errors on the accuracy of the inverse analysis are investigated. Two optimization... 

In this paper, some important operating parameters of nuclear power plants (NPPs) transients are forecasted using different supervised learning methods including feed-forward back propagation (FFBP) neural networks such as cascade feed-forward neural network (CFFNN), statistical methods such as support vector regression (SVR), and localized networks such as radial basis network (RBN). Different learning algorithms, including gradient descent (GD), gradient descent with momentum (GDM), scaled conjugate gradient (SCG), Levenberg-Marquardt (LM), and Bayesian regularization (BR) are used in CFFNN method. SVR method is used with different kernel functions including Gaussian, polynomial, and... 

In the last years, an appreciable effort has been directed toward developing empirical models to link the relative permeability of gas condensate reservoirs to the interfacial tension and velocity as well as saturation. However, these models suffer from non-universality and uncertainties in setting the tuning parameters. In order to alleviate the aforesaid infirmities in this study, comprehensive modeling was carried out by employing numerous smart computer-aided algorithms including Support Vector Regression (SVR), Least Square Support Vector Machine (LSSVM), Extreme Learning Machine (ELM), Multilayer Perceptron (MLP), Group Method of Data Handling (GMDH), and Gene Expression Programming...