Recently, several modification techniques have been introduced to the line search bfgsmethod for solving unconstrained optimization problems. We present a modified bfgs method for solving symmetric nonlinear equation...
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Recently, several modification techniques have been introduced to the line search bfgsmethod for solving unconstrained optimization problems. We present a modified bfgs method for solving symmetric nonlinear equations. The numerical results show that the approach to be reliable and efficient.
Based on some new interpolation conditions, a quadratic interpolation model is constructed to approximate the objective function, and then a class of modified bfgs methods with function value information is presented....
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Based on some new interpolation conditions, a quadratic interpolation model is constructed to approximate the objective function, and then a class of modified bfgs methods with function value information is presented. The new methods satisfy some new weak secant equations and there is a parameter gamma in the update formulae which ranges from zero to one. The global and local superlinear convergence properties of the new modified bfgs methods are proved. Numerical results for standard test problems from CUTE are reported, which indicate that all the methods in the proposed class perform well. Ensuring the sufficient positive definiteness of the updating matrices, an adaptive bfgs quasi-Newton method by dynamically choosing the parameter gamma is proposed, which may be competitive with other bfgs modifications.
Based on the modified bfgs method proposed by Li and Fukushima (2001), we present a new value of the parameter t in Dai-Liao Conjugate Gradient method. Under mild assumptions, we establish the global convergence prope...
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Based on the modified bfgs method proposed by Li and Fukushima (2001), we present a new value of the parameter t in Dai-Liao Conjugate Gradient method. Under mild assumptions, we establish the global convergence property of the proposed method. Numerical results on some test problems in the CUTEst library illustrate computational efficiency of the new method. (C) 2019 Published by Elsevier B.V.
We present a joint inversion method for the transmitter navigation and the seafloor resistivity for frequency domain marine controlled-source electromagnetic (CSEM) data. The inversion approach is based on the modifie...
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We present a joint inversion method for the transmitter navigation and the seafloor resistivity for frequency domain marine controlled-source electromagnetic (CSEM) data. The inversion approach is based on the modifiedbfgs scheme, which has an advantage that one can update the Hessian matrix by using the bfgs scheme rather than computing the Hessian matrix itself during the inversion process. The partial derivatives of the electromagnetic field responses with respect to both the seafloor resistivity and the transmitter navigation parameters including the azimuth, dip and horizontal positions of the transmitter antenna are analytically calculated. We invert for both the navigation parameters of the towed dipole source (including antenna azimuth, dip, and horizontal positions) and seafloor resistivity by using the whole range of data instead of the near-field data (usually source-receiver offset <1 km). An eigenparameter analysis shows that seafloor resistivities and transmitter navigation parameters can be independently resolved, and a better reconstruction can be obtained with multiple frequency data. The inversions of both the synthetical and field data sets indicate that our inversion method can simultaneously reconstruct seafloor resistivity structures and transmitter navigation parameters. (C) 2016 Elsevier B.V. All rights reserved.
Based on two modified secant equations proposed by Yuan, and Li and Fukushima, we extend the approach proposed by Andrei, and introduce two hybrid conjugate gradient methods for unconstrained optimization problems. Ou...
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Based on two modified secant equations proposed by Yuan, and Li and Fukushima, we extend the approach proposed by Andrei, and introduce two hybrid conjugate gradient methods for unconstrained optimization problems. Our methods are hybridizations of Hestenes-Stiefel and Dai-Yuan conjugate gradient methods. Under proper conditions, we show that one of the proposed algorithms is globally convergent for uniformly convex functions and the other is globally convergent for general functions. To enhance the performance of the line search procedure, we propose a new approach for computing the initial value of the steplength for initiating the line search procedure. We give a comparison of the implementations of our algorithms with two efficiently representative hybrid conjugate gradient methods proposed by Andrei using unconstrained optimization test problems from the CUTEr collection. Numerical results show that, in the sense of the performance profile introduced by Dolan and Mor,, the proposed hybrid algorithms are competitive, and in some cases more efficient.
In geotechnical engineering, based on the theory of inverse analysis of displacement, the problem for identification of material parameters can be transformed into an optimization problem. Commonly, because of the non...
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ISBN:
(纸本)9780878493999
In geotechnical engineering, based on the theory of inverse analysis of displacement, the problem for identification of material parameters can be transformed into an optimization problem. Commonly, because of the non-linear relationship between the identified parameters and the displacement, the objective function bears the multimodal characteristic in the variable space. So to solve better the multimodal characteristic in the non-linear inverse analysis, a new global optimization algorithm, which integrates the dynamic descent algorithm and the modifiedbfgs (Brogden-Fietcher-Goldfrab-Shanno) algorithm, is proposed. Five typical multimodal functions in the variable space are tested to prove that the new proposed algorithm can quickly converge to the best point with few function evaluations. In the practical application, the new algorithm is employed to identify the Young's modulus of four different materials. The results of the identification further show that the new proposed algorithm is a very highly efficient and robust one.
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