Spectral Conjugate Gradient Research Articles

A new spectral conjugate gradient method with descent condition and global convergence property for unconstrained optimization

A new spectral conjugate gradient method with descent condition and global convergence property for unconstrained optimization

A Novel Method of Dynamic Force Identification and Its Application

In this paper, an efficient mixed spectral conjugate gradient (EMSCG, for short) method is presented for solving unconstrained optimization problems. In this work, we construct a novel formula performed by using a conjugate gradient parameter which takes into account the advantages of Fletcher–Reeves (FR), Polak–Ribiere–Polyak (PRP), and a variant Polak-Ribiere-Polyak (VPRP), prove its stability and convergence, and apply it to the dynamic force identification of practical engineering structure. The analysis results show that the present method has higher efficiency, stronger robust convergence quality, and fewer iterations. In addition, the proposed method can provide more efficient and numerically stable approximation of the actual force, compared with the FR method, PRP method, and VPRP method. Therefore, we can make a clear conclusion that the proposed method in this paper can provide an effective optimization solution. Meanwhile, there is reason to believe that the proposed method can offer a reference for future research.

Descent Condition for a Scalar Parameter of Spectral HS (SpHS) Conjugate Gradient Method

Spectral conjugate gradient method has been used in most cases as an alternative to the conjugate gradient (CG) method in order to solve nonlinear unconstrained problems. In this paper, we introduced a spectral parameter of HS conjugate gradient method resultant from the classical CG search direction and used some of the standard test functions with numerous variables to prove its sufficient descent and global convergence properties, the numerical outcome is verified by exact line search procedures.

Optimization Techniques to Deeply Mine the Transcriptomic Profile of the Sub-Genomes in Hybrid Fish Lineage.

It has been shown that reciprocal cross allodiploid lineage with sub-genomes derived from the cross of Megalobrama amblycephala (BSB) × Culter alburnus (TC) generates the variations in phenotypes and genotypes, but it is still a challenge to deeply mine biological information in the transcriptomic profile of this lineage owing to its genomic complexity and lack of efficient data mining methods. In this paper, we establish an optimization model by non-negative matrix factorization approach for deeply mining the transcriptomic profile of the sub-genomes in hybrid fish lineage. A new so-called spectral conjugate gradient algorithm is developed to solve a sequence of large-scale subproblems such that the original complicated model can be efficiently solved. It is shown that the proposed method can provide a satisfactory result of taxonomy for the hybrid fish lineage such that their genetic characteristics are revealed, even for the samples with larger detection errors. Particularly, highly expressed shared genes are found for each class of the fish. The hybrid progeny of TC and BSB displays significant hybrid characteristics. The third generation of TC-BSB hybrid progeny ( and ) shows larger trait separation.

Spectral modified Polak–Ribiére–Polyak projection conjugate gradient method for solving monotone systems of nonlinear equations

In this paper, we present a modification of Polak–Ribie´re–Polyak (PRP) conjugate gradient method for solving system of monotone nonlinear equations which is a combination of spectral conjugate gradient method and the hyperplane projection technique. The method is based on two methods for unconstrained optimization proposed by Wan et al. (2011) and Sun (2015). We obtained a new search direction by the use of a different formula for the conjugate gradient parameter. The search direction satisfies the sufficient descent condition and the global convergence of the method is established under some assumptions. Preliminary numerical comparison with some existing methods shows the efficiency of the proposed method.

A modified conjugate gradient method for monotone nonlinear equations with convex constraints

In this paper, a modified Hestenes-Stiefel (HS) spectral conjugate gradient (CG) method for monotone nonlinear equations with convex constraints is proposed based on projection technique. The method can be viewed as an extension of a modified HS-CG method for unconstrained optimization proposed by Amini et al. (Optimization Methods and Software, pp: 1-13, 2018). A new search direction is obtained by incorporating the idea of spectral gradient parameter and some modification of the conjugate gradient parameter. The proposed method is derivative-free and requires low memory which makes it suitable for large scale monotone nonlinear equations. Global convergence of the method is established under suitable assumptions. Preliminary numerical comparisons with some existing methods are given to show the efficiency of our proposed method. Furthermore, the proposed method is successfully applied to solve sparse signal reconstruction in compressive sensing.

A Modified Spectral Conjugate Gradient Method with Global Convergence

In this paper, a modified version of the spectral conjugate gradient algorithm suggested by Jian, Chen, Jiang, Zeng and Yin is proposed. It is proved that the new method is globally convergent for ...

A new conjugate gradient method based on Quasi-Newton equation for unconstrained optimization

The spectral conjugate gradient method is an effective method for large-scale unconstrained optimization problems. In this paper, based on Quasi-Newton direction and Quasi-Newton equation, a new spectral conjugate gradient method is proposed. This method is motivated by the three-term modified Polak-Ribiyre-Polyak (PRP) method and spectral parameters. The global convergence of algorithm is proved for general functions under a strong Wolfe line search. Numerical results show that the new algorithm is superior to the three-term modified PRP method.

A spectral conjugate gradient method for solving large-scale unconstrained optimization

This paper establishes a spectral conjugate gradient method for solving unconstrained optimization problems, where the conjugate parameter and the spectral parameter satisfy a restrictive relationship. The search direction is sufficient descent without restarts in per-iteration. Moreover, this feature is independent of any line searches. Under the standard Wolfe line searches, the global convergence of the proposed method is proved when |βk|≤βkFR holds. The preliminary numerical results are presented to show effectiveness of the proposed method.

Some improvement strategies for the time-domain dual-sensor full waveform inversion

Full waveform inversion (FWI) is an effective method in retrieving high-resolution subsurface parameters from seismic data. In this paper, we review the dual-sensor FWI previously studied and present some improvement strategies. We first modify the low-pass Wiener filter to band-pass Wiener filter for time-domain FWI to reduce the overlapped regions. Secondly, we use spectral conjugate gradient method to update the models instead of the conventional conjugate gradient method to speed up the convergence and improve the inversion accuracy. At last, we further improve the efficient boundary storage method which is suitable for the first-order velocity-stress acoustic wave equation to reduce the storage burden. After that, we validate these new strategies for the modified Marmousi model, and the synthetic example shows the feasibility and robustness of these new strategies in terms of improving computational efficiency and alleviating large amounts of data storage.

A new spectral conjugate gradient method and ARIMA combined forecasting model and application

It is of great practical significance to fit and predict actual time series. Based on the theories of time series analysis and unconstrained optimization, a new spectral conjugate gradient method–autoregressive integrated moving average combined model (FHS spectral CG–ARIMA combined model) is proposed to fit and predict the actual time series. First, combining the characteristics and advantages of different CG methods, we propose Fang–Hestenes–Stiefel algorithm (FHS). FHS satisfies the automatic descent property and has global convergence under the reasonable assumptions and Wolfe search. Second, many numerical results have been given there: compared with other related algorithms, FHS algorithm has obvious advantages. Third, FHS spectral CG–ARIMA combined model is given in detail. Fourth, the combined model is applied to fit the actual time series and the fitting effect is found to be remarkable.

A New Globally Convergent of Spectral Hideaki - Yasushi Type Conjugate Gradient Method

This paper presents two new spectral conjugate gradient methods which are designed for solving nonlinear unconstrained optimization problems. These methods are based on the idea of the Hideaki – Yasushi method. Which produce sufficient descent search direction at every iteration. Experimental results indicate that the new proposed methods more efficient than the Hideaki – Yasush method

A Global Convergence of Spectral Conjugate Gradient Method for Large Scale Optimization

A Global Convergence of Spectral Conjugate Gradient Method for Large Scale Optimization

A modified spectral conjugate gradient projection method for signal recovery

In this paper, signal recovery problems are first reformulated as a nonlinear monotone system of equations such that the modified spectral conjugate gradient projection method proposed by Wan et al. can be extended to solve the signal recovery problems. In view of the equations’ analytic properties, an improved projection-based derivative-free algorithm (IPBDF) is developed. Compared with the similar algorithms available in the literature, an advantage of IPBDF is that the search direction is always sufficiently descent as well as being close to the quasi-Newton direction, without requirement of computing the Jacobian matrix. Then, IPBDF is applied into solving a number of test problems for reconstruction of sparse signals and blurred images. Numerical results indicate that the proposed method either can recover signals in less CPU time or can reconstruct the images with higher quality than the other similar ones.

A New Spectral Conjugate Gradient Algorithm for Unconstrained Optimization

A New Spectral Conjugate Gradient Algorithm for Unconstrained Optimization

Extended Dai-Yuan conjugate gradient strategy for large-scale unconstrained optimization with applications to compressive sensing

We present a new spectral conjugate gradient method based on the Dai-Yuan strategy to solve large-scale unconstrained optimization problems with applications to compressive sensing. In our method, the numerator of conjugate gradient parameter is a convex combination from the maximum gradient norm value in some preceding iterates and the current gradient norm value. This combination will try to produce the larger step-size far away from the optimizer and the smaller step-size close to it. In addition, the spectral parameter guarantees the descent property of the new generated direction in each iterate. The global convergence results are established under some standard assumptions. Numerical results are reported which indicate the promising behavior of the new procedure to solve large-scale unconstrained optimization and compressive sensing problems.

A spectral conjugate gradient method for nonlinear inverse problems

In this study, a new spectral conjugate gradient method is presented to solve nonlinear inverse problems, which transferred into the unconstrained nonlinear optimization with a neighbour term. The global convergence and regularizing properties of the proposed method are analysed. In the end, some numerical results illustrate the efficiency and the robustness of this method.

Two modified spectral conjugate gradient methods and their global convergence for unconstrained optimization

ABSTRACTIn this paper, two modified spectral conjugate gradient methods which satisfy sufficient descent property are developed for unconstrained optimization problems. For uniformly convex problems, the first modified spectral type of conjugate gradient algorithm is proposed under the Wolfe line search rule. Moreover, the search direction of the modified spectral conjugate gradient method is sufficiently descent for uniformly convex functions. Furthermore, according to the Dai–Liao's conjugate condition, the second spectral type of conjugate gradient algorithm can generate some sufficient decent direction at each iteration for general functions. Therefore, the second method could be considered as a modification version of the Dai–Liao's algorithm. Under the suitable conditions, the proposed algorithms are globally convergent for uniformly convex functions and general functions. The numerical results show that the approaches presented in this paper are feasible and efficient.

Two new spectral conjugate gradient algorithms based on Hestenes–Stiefel

The spectral conjugate gradient algorithm, which is a variant of conjugate gradient method, is one of the effective methods for solving unconstrained optimization problems. In this paper, based on Hestenes–Stiefel method, two new spectral conjugate gradient algorithms (Descend Hestenes-Stiefel (DHS) and Wang-Hestenes-Stiefel (WHS)) are proposed. Under Wolfe line search and mild assumptions on objective function, the two algorithms possess sufficient descent property without any other conditions and are always globally convergent. Numerical results turn out the new algorithms outperform Hestenes–Stiefel conjugate gradient method.

Spatial-Temporal Separation Based on the Dynamic Recurrent Wavelet Neural Network Modelling for ASP Flooding

In this paper, a three-dimensional spatial-temporal decomposition modelling method is proposed to build the alkali-surfactant-polymer (ASP) flooding model, in which a new dynamic recurrent wavelet neural network (DRWNN) is presented to identify the temporal coefficients. At first, the detailed mathematical model of ASP flooding is described which is a complex distributed parameter system. Then a three-dimensional spatial-temporal modelling method is inferred based on Karhunen-Loeve (K-L) decomposition to decompose the water saturation of reservoir into a series of spatial basis functions and corresponding temporal coefficients. Furthermore, the recurrent wavelet neural network is used to acquire the identification model, in which the injection concentrations of ASP flooding and temporal coefficients are taken as the input and output information. In order to improve the capability of dynamic modelling, DRWNN is proposed through adding feedback layers and setting the different weights with time to achieve dynamic memory of the past information. Considering the gradient descent method for the neural networks training easily leads to local minimum and slow convergence speed, the spectral conjugate gradient method is introduced to optimize the weights of DRWNN. At last, DRWNN is used to build the relation between the moisture content of production wells and the water saturation of the corresponding grids. Thus, the final approximate model of ASP flooding is finished. The accuracy is proved by model with four injection wells and nine production wells through data from the mechanism model.