Convergence rate of the modified Levenberg-Marquardt method under Hölderian local error bound
نویسندگان
چکیده
Abstract In this article, we analyze the convergence rate of modified Levenberg-Marquardt (MLM) method under Hölderian local error bound condition and continuity Jacobian, which are more general than Lipschitz Jacobian. Under special circumstances, MLM coincides with results presented by Fan. A globally convergent algorithm trust region technique will also be given.
منابع مشابه
Convergence Properties of a Self-adaptive Levenberg-Marquardt Algorithm Under Local Error Bound Condition
We propose a new self-adaptive Levenberg-Marquardt algorithm for the system of nonlinear equations F(x) = 0. The Levenberg-Marquardt parameter is chosen as the product of ‖Fk‖ with δ being a positive constant, and some function of the ratio between the actual reduction and predicted reduction of the merit function. Under the local error bound condition which is weaker than the nonsingularity, w...
متن کاملLocal convergence of Levenberg–Marquardt methods under Hölder metric subregularity
We describe and analyse Levenberg–Marquardt methods for solving systems of nonlinear equations. More specifically, we first propose an adaptive formula for the Levenberg–Marquardt parameter and analyse the local convergence of the method under Hölder metric subregularity. We then introduce a bounded version of the Levenberg–Marquardt parameter and analyse the local convergence of the modified m...
متن کاملOn a Global Complexity Bound of the Levenberg-Marquardt Method
In this paper, we propose a new updating rule of the LevenbergMarquardt (LM) parameter for the LM method for nonlinear equations. We show that the global complexity bound of the new LM algorithm is O( −2), that is, it requires at most O( −2) iterations to derive the norm of the gradient of the merit function below the desired accuracy . Host: Jiawang Nie Wednesday, November 1, 2017 4:00 PM AP&M...
متن کاملConvergence Rate of The Trust Region Method for Nonlinear Equations Under Local Error Bound Condition
In this paper, we present a new trust region method for nonlinear equations with the trust region converging to zero. The new method preserves the global convergence of the traditional trust region methods in which the trust region radius will be larger than a positive constant. We study the convergence rate of the new method under the local error bound condition which is weaker than the nonsin...
متن کاملA Modified Levenberg-Marquardt Method for the Bidirectional Relay Channel
This paper presents an optimization approach for a system consisting of multiple bidirectional links over a two-way amplify-and-forward relay. It is desired to improve the fairness of the system. All user pairs exchange information over one relay station with multiple antennas. Due to the joint transmission to all users, the users are subject to mutual interference. A mitigation of the interfer...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Open Mathematics
سال: 2022
ISSN: ['2391-5455']
DOI: https://doi.org/10.1515/math-2022-0485