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A Note on the Global Convergence of the Quadratic Hybridization of Polak-Ribiere-Polyak and Fletcher-Reeves conjugate gradient Methods

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2013年第1期157卷 297-298页

作者： Babaie-Kafaki, Saman Semnan Univ Dept Math Fac Math Stat & Comp Sci Semnan Iran

A revision on condition (27) of Lemma 3.2 of Babaie-Kafaki (J. Optim. Theory Appl. 154(3):916-932, 2012) is made. Throughout, we use the same notation and equation numbers as in Babaie-Kafaki (J. Optim. Theory Appl. 1... 详细信息

关键词： Unconstrained optimization conjugate gradient algorithm Global convergence

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A Note on Global Convergence Result for conjugate gradient Methods

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Journal of Shanghai University(English Edition) 2001年第1期5卷 15-19页

作者： BAI Yan qin Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200436, China Department of Mathematics College of Sciences Shanghai University Shanghai China

We extend a results presented by Y.F. Hu and *** (1991) [1] on the global convergence result for conjugate gradient methods with different choices for the parameter β k . In this note, the conditions ... 详细信息

关键词： conjugate gradient algorithm descent property global convergence restarting

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conjugate gradient Acceleration of Non-Linear Smoothing Filters

Conjugate Gradient Acceleration of Non-Linear Smoothing Filt...

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3rd IEEE Global Conference on Signal and Information Processing (GlobalSIP)

作者： Knyazev, Andrew Malyshev, Alexander MERL 201 Broadway8th Floor Cambridge MA 02139 USA

ISBN: (纸本)9781479975914

The most efficient signal edge-preserving smoothing filters, e.g., for denoising, are non-linear. Thus, their acceleration is challenging and is often performed in practice by tuning filter parameters, such as by increasing the width of the local smoothing neighborhood, resulting in more aggressive smoothing of a single sweep at the cost of increased edge blurring. We propose an alternative technology, accelerating the original filters without tuning, by running them through a special conjugate gradient method, not affecting their quality. The filter non-linearity is dealt with by careful freezing and restarting. Our initial numerical experiments on toy onedimensional signals demonstrate 20x acceleration of the classical bilateral filter and 3-5x acceleration of the recently developed guided filter.

关键词： conjugate gradient algorithm edge-preserving denoising low-pass filters

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Hybrid conjugate gradient Methods Based on an Extended Least-Squares Model

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VIETNAM JOURNAL OF MATHEMATICS 2024年 1-9页

作者： Toofan, Mariya Babaie-Kafaki, Saman Semnan Univ Dept Math POB 35195363 Semnan Iran Free Univ Bozen Bolzano Fac Engn I-39100 Bolzano Italy

In order to simultaneously benefit the computational merits of the Hestenes-Stiefel method and the worthwhile descent and convergence properties of the Dai-Yuan method, Andrei (Stud. Inform. Control 17, 55-70, 2008) introduced a hybrid conjugate gradient algorithm by convexly combining the parameters of the two methods. Here, on account of the advantages of the convex combinations of the conjugate gradient methods, three hybrid conjugate gradient algorithms are proposed by using the ellipsoid norm (as an extension of the Euclidean norm) in a least-squares framework. To determine the hybridization parameter of the given methods, quasi-Newton aspects are also employed, including the secant equation as well as the memoryless (inverse) Hessian updating formulas. The computational advantages of the given algorithms are depicted on a set of CUTEr test functions.

关键词： Unconstrained optimization conjugate gradient algorithm Least-squares model Ellipsoid norm Secant condition

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conjugate gradient persymmetric adaptive matched filter

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DIGITAL SIGNAL PROCESSING 2022年第0期123卷 103395-103395页

作者： Lin, Jie Jiang, Chaoshu Jiang, Jiahua Kang, Jiawen Univ Elect Sci & Technol China Sch Informat & Commun Engn Chengdu 611731 Sichuan Peoples R China ShanghaiTech Univ Sch Informat Sci & Technol Shanghai 201210 Peoples R China

The rank corresponding to interferences and clutter is commonly much smaller than the size of the covariance matrix due to the sparsity of detection environment, which results in the approximate low rank correction structure of the transformed estimated covariance matrix in the persymmetric adaptive matched filter (PS-AMF). As a result, the conjugate gradient (CG) algorithm is an efficient iterative algorithm in the calculation of the weight vector of PS-AMF and produces the projection of PS-AMF weight vector to the Krylov subspace with the dimension increasing with the CG iterations. Therefore, we focus on the case that CG algorithm is used in PS-AMF in this paper, which leads to a family of reduced-rank detectors in Krylov subspace for PS-AMF. These detectors are referred to as the CG-PS-AMF detectors. Firstly, the expected value of the output signal-to-interference-and-noise ratio (SINR) of CG-PSAMF detector is analyzed, and then its approximation expression is given. Finally, numerical results are presented to verify our theoretical analysis of CG-PS-AMF. Meanwhile, compared with its counterparts, CG-PS-AMF detector shows better detection performance. Besides, it is shown that CG-PS-AMF has a low computational cost.& nbsp;(C)& nbsp;2022 Elsevier Inc. All rights reserved.

关键词： conjugate gradient algorithm Persymmetric adaptive matched filter Output signal-to-interference-and-noise ratio Krylov subspace

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Krylov subspace method based on data preprocessing technology

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Journal of Systems Engineering and Electronics 2008年第6期19卷 1063-1069页

作者： Tang Bin Wang Xuegang Zhang Chaoshen Chen Kesong School of Electronic Engineering Univ. of Electronic Science and Technology of China Chengdu 610054 P. R. China Chengdu Aircraft Design & Research Inst. Chengdu 610041 P. R. China

The performance of adaptive beamforming techniques is limited by the nonhomogeneous clutter scenario. An augmented Krylov subspace method is proposed, which utilizes only a single snapshot of the data for adaptive processing. The novel algorithm puts together a data preprocessor and adaptive Krylov subspace algorithm, where the data preprocessor suppresses discrete interference and the adaptive Krylov subspace algorithm suppresses homogeneous clutter. The novel method uses a single snapshot of the data received by the array antenna to generate a cancellation matrix that does not contain the signal of interest （SOI） component, thus, it mitigates the problem of highly nonstationary clutter environment and it helps to operate in real-time. The benefit of not requiring the training data comes at the cost of a reduced degree of freedom （DOF） of the system. Simulation illustrates the effectiveness in clutter suppression and adaptive beamforming. The numeric results show good agreement with the proposed theorem.

关键词： adaptive beamforming Krylov subspace conjugate gradient algorithm nonhomogeneous clutter clutter suppress

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SINE TRANSFORM MATRIX FOR SOLVING TOEPLITZ MATRIX PROBLEMS

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Journal of Computational Mathematics 2001年第2期19卷 167-176页

作者： Li-zhi Cheng (Department of Mathematics & System Sciences, National University of Defence Technology, Changsha 410073, China) 国防科技大学湖南长沙 410073

Provides information on a study which discussed the properties of eigenvalues for the solutions of symmetric positive definite Toeplitz systems, skew circulant and sine transform based properties. Eigenvalues of various preconditioners; Design of positive sine transform based preconditioners; Clustering property of the preconditioners; Numerical results.

关键词： preconditioner Toeplitz systems the fast sine transform conjugate gradient algorithm

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Unmagnetized plasma media parameters reconstruction using FDTD and gradient-based minimization method

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INTERNATIONAL JOURNAL OF NUMERICAL MODELLING-ELECTRONIC NETWORKS DEVICES AND FIELDS 2020年第2期33卷

作者： Deng, Haochuan Shi, Lijuan Feng, Xuejian Wei, Xiao Yin, Hongcheng Univ China Dept Informat Engn Commun Beijing 100089 Peoples R China Sci & Technol Electromagnet Scattering Lab Beijing Peoples R China Jiangsu Univ Sch Sci Zhenjiang Jiangsu Peoples R China

A time-domain inverse scattering algorithm for determining unknown plasma resonance frequency and electron collision frequency of unmagnetized plasma media object has been proposed. Finite-difference time-domain (FDTD) method in conjunction with Lagrange multipliers and gradient-based minimization method are used in the proposed algorithm. The reconstruction of the parameters is based on the minimization of a cost function that describes the discrepancy between simulation and measured data of the electric field at the observation points. In order to obtain the gradient value of the unknown plasma parameters, an augmented cost function has been given by means of Lagrange multipliers with the Maxwell curl equations and constitutive relation of the unmagnetized plasma media. Then, the gradient value could be obtained after a series of transformations. At last, the Ploak-Ribiere conjugate gradient algorithm has been applied to update the plasma parameters iteratively. The effectiveness of the proposed algorithm has been validated through the simulation test.

关键词： conjugate gradient algorithm finite difference time domain inverse scattering unmagnetized plasma media

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DEVELOPMENTS IN STRUCTURAL ANALYSIS BY DIRECT ENERGY MINIMIZATION

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AIAA JOURNAL 1968年第6期6卷 1036-&页

作者： FOX, RL STANTON, EL Case Western Reserve University Cleveland Ohio

The equivalence of problems in structural analysis to certain variational statements has traditionally been used as a means of formulating field equations and natural boundary conditions. In recent years developments in computers and minimization algorithms have made it possible to determine the displacement state that satisfies the variational principle without direct recourse to the solution of a system of equations. In this paper an unconstrained minimization approach is applied to a problem in finite-element structural analysis and is shown numerically to be competitive with conventional methods. Adopting an energyminimization viewpoint, important storage advantages of the conjugate-gradient method are extended by eliminating the need for an assembled stiffness matrix. The convergence of conjugate direction methods in quadratic problems is shown to be greatly influenced by scale effects. This problem is studied using the eigenvalues of the stiffness matrix and a practical solution is proposed which by a special scaling transformation can improve the ratio of the maximum to the minimum eigenvalue by several orders of magnitude. This transformation is applied with considerable success to a plate-bending problem. © 1968 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Structural Analysis Finite Element Method conjugate gradient Method Aspect Ratio Material Properties Plane Stress conjugate gradient algorithm Flexible Structures Taylor Series Trusses

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Efficient Monolithic Solution algorithm for High-Fidelity Aerostructural Analysis and Optimization

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AIAA JOURNAL 2018年第3期56卷 1251-1265页

作者： Zhang, Zimi J. Zingg, David W. Univ Toronto Inst Aerosp Studies 4925 Dufferin St Toronto ON M3H 5T6 Canada Univ Toronto Inst Aerosp Studies Computat Aerodynam & Sustainable Aviat Toronto ON M3H 5T6 Canada

An efficient and robust solution algorithm for the aerostructural analysis and coupled adjoint problems is crucial to the success of high-fidelity aerostructural optimization. The objective of the present paper is to investigate ways to maximize the efficiency of a monolithic solution method and further quantify its benefits in the context of aerostructural optimization. A Newton-Krylov method is used for the aerostructural analysis, and a preconditioned Krylov subspace method is used for the coupled adjoint solution. Several aspects of the monolithic solution method have been investigated. These include appropriate strategies for scaling and matrix-vector product evaluations as well as block Jacobi and block Gauss-Seidel preconditioning techniques that preserve the modularity between subproblems. The monolithic solution method is applied to problems with varying degrees of fluid-structure coupling as well as a wing-span optimization study. In most cases, the monolithic solution algorithm requires 20-70% less computing time than its partitioned counterpart. This advantage increases with increasing wing flexibility. Robustness of the monolithic solution method is shown via its reduced sensitivity to the choice of problem-dependent solution parameters as well as its ability to converge when the partitioned method fails.

关键词： conjugate gradient algorithm Wing Span Computing Time Finite Element Analysis Iterative Solution Freestream Mach Number FSI Structural Failure Young's Modulus Structural Modeling

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