The Levenberg-Marquardt method, the best algorithm to obtain the least-square solution of nonlinear equations, is applied to calculate the stable phase equilibria. It can get the best combination between robustness an...The Levenberg-Marquardt method, the best algorithm to obtain the least-square solution of nonlinear equations, is applied to calculate the stable phase equilibria. It can get the best combination between robustness and speed of the calculations. Its application to ternary Al-Si-Mg system is executed in detail. The calculated phase equilibria agree well with the experimental results. Furthermore, the Levenberg-Marquardt method is not sensitive to the initial values.展开更多
In this paper, a new method for solving a mathematical programming problem with linearly complementarity constraints (MPLCC) is introduced, which applies the Levenberg-Marquardt (L-M) method to solve the B-stationary ...In this paper, a new method for solving a mathematical programming problem with linearly complementarity constraints (MPLCC) is introduced, which applies the Levenberg-Marquardt (L-M) method to solve the B-stationary condition of original problem. Under the MPEC-LICQ, the proposed method is proved convergent to B-stationary point of MPLCC.展开更多
To save the calculations of Jacobian,a multi-step Levenberg-Marquardt method named Shamanskii-like LM method for systems of nonlinear equations was proposed by Fa.Its convergence properties have been proved by using a...To save the calculations of Jacobian,a multi-step Levenberg-Marquardt method named Shamanskii-like LM method for systems of nonlinear equations was proposed by Fa.Its convergence properties have been proved by using a trust region technique under the local error bound condition.However,the authors wonder whether the similar convergence properties are still true with standard line searches since the direction may not be a descent direction.For this purpose,the authors present a new nonmonotone m-th order Armijo type line search to guarantee the global convergence.Under the same condition as trust region case,the convergence rate also has been shown to be m+1 by using this line search technique.Numerical experiments show the new algorithm can save much running time for the large scale problems,so it is efficient and promising.展开更多
As applying the Levenberg-Marquardt method to the reformulation of linear complementarity problem,a modulus-based Levenberg-Marquardt method with non-monotone line search is established and the global convergence resu...As applying the Levenberg-Marquardt method to the reformulation of linear complementarity problem,a modulus-based Levenberg-Marquardt method with non-monotone line search is established and the global convergence result is presented.Numerical experiments show that the proposed method is efficient and outperforms the modulus-based matrix splitting iteration method.展开更多
We propose an inexact affine scaling Levenberg-Marquardt method for solving bound-constrained semismooth equations under the local error bound assumption which is much weaker than the standard nonsingularity condition...We propose an inexact affine scaling Levenberg-Marquardt method for solving bound-constrained semismooth equations under the local error bound assumption which is much weaker than the standard nonsingularity condition. The affine scaling Levenberg-Marquardt equation is based on a minimization of the squared Euclidean norm of linearized model adding a quadratic affine scaling matrix to find a solution which belongs to the bounded constraints on variable. The global convergence and the superlinear convergence rate are proved.Numerical results show that the new algorithm is efficient.展开更多
基金This research is supported by the State Key Fundamental Research Project(G2000067202-1).
文摘The Levenberg-Marquardt method, the best algorithm to obtain the least-square solution of nonlinear equations, is applied to calculate the stable phase equilibria. It can get the best combination between robustness and speed of the calculations. Its application to ternary Al-Si-Mg system is executed in detail. The calculated phase equilibria agree well with the experimental results. Furthermore, the Levenberg-Marquardt method is not sensitive to the initial values.
文摘In this paper, a new method for solving a mathematical programming problem with linearly complementarity constraints (MPLCC) is introduced, which applies the Levenberg-Marquardt (L-M) method to solve the B-stationary condition of original problem. Under the MPEC-LICQ, the proposed method is proved convergent to B-stationary point of MPLCC.
基金supported by the Natural Science Foundation of Anhui Province under Grant No.1708085MF159the Natural Science Foundation of the Anhui Higher Education Institutions under Grant Nos.KJ2017A375+1 种基金KJ2019A0604the abroad visiting of excellent young talents in universities of Anhui province under Grant No.GXGWFX2019022。
文摘To save the calculations of Jacobian,a multi-step Levenberg-Marquardt method named Shamanskii-like LM method for systems of nonlinear equations was proposed by Fa.Its convergence properties have been proved by using a trust region technique under the local error bound condition.However,the authors wonder whether the similar convergence properties are still true with standard line searches since the direction may not be a descent direction.For this purpose,the authors present a new nonmonotone m-th order Armijo type line search to guarantee the global convergence.Under the same condition as trust region case,the convergence rate also has been shown to be m+1 by using this line search technique.Numerical experiments show the new algorithm can save much running time for the large scale problems,so it is efficient and promising.
基金This research is supported by National Science Foundation of China(41725017)National Basic Research Program of China under grant number 2014CB845906+1 种基金It is also partially supported by the CAS/CAFEA international partnership Program for creative research teams(No.KZZD-EW-TZ-19 and KZZD-EW-TZ-15)Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDB18010202)。
文摘As applying the Levenberg-Marquardt method to the reformulation of linear complementarity problem,a modulus-based Levenberg-Marquardt method with non-monotone line search is established and the global convergence result is presented.Numerical experiments show that the proposed method is efficient and outperforms the modulus-based matrix splitting iteration method.
基金Acknowledgments. This work is supported by the National Natural Science Foundation of China under projects Nos. 11071029, 11101064 and 91130007 and speciMized Research Fund for the Doctoral Program of Higher Education （20110041120039）. We are grateful to the associate editor and anonymous referee＇s comments to improve the quality of the manuscript. The second author also appreciate the discussion with his student Miao Xiaonan.
基金Supported by National Natural Science Foundation of China(No.11571074)Scientific Research Fund of Hunan Provincial Education Department(No.18A351,17C0393)Natural Science Foundation of Hunan Province(No.2019JJ50105)
文摘We propose an inexact affine scaling Levenberg-Marquardt method for solving bound-constrained semismooth equations under the local error bound assumption which is much weaker than the standard nonsingularity condition. The affine scaling Levenberg-Marquardt equation is based on a minimization of the squared Euclidean norm of linearized model adding a quadratic affine scaling matrix to find a solution which belongs to the bounded constraints on variable. The global convergence and the superlinear convergence rate are proved.Numerical results show that the new algorithm is efficient.
