scholarly journals On the convergence of the modified Levenberg–Marquardt method with a nonmonotone second order Armijo type line search

2013 ◽  
Vol 239 ◽  
pp. 152-161 ◽  
Author(s):  
Weijun Zhou
Keyword(s):  
Line Search ◽  
Second Order ◽  
Marquardt Method ◽  
Levenberg Marquardt

Non-Linear Least-Square Optimization of Mechanisms Based on Levenberg-Marquardt Method

2008 ◽  
Author(s):  
Ramon Sancibrian ◽  
Ana De-Juan ◽  
Fernando Viadero
Keyword(s):  
Jacobian Matrix ◽  
Hessian Matrix ◽  
Optimization Method ◽  
Second Order ◽  
Least Square ◽  
Marquardt Method ◽  
Design Variables ◽  
Levenberg Marquardt ◽  
Pseudo Second Order ◽  
Linear Least Square

One of the main problems to improve the convergence rate in deterministic optimization of mechanisms is to obtain the Hessian matrix. The required second-order derivatives are difficult to obtain or they are not available. Levenberg-Marquardt optimization method is a pseudo-second order method which means that uses the jacobian information to estimate the Hessian matrix. In this paper, the formulation to obtain the exact form of the jacobian matrix is presented and how can be implemented in the Levenberg-Marquardt method. This formulation gives a very effective method to optimize mechanism geometry considering a large number of prescribed positions and design variables. At the same time it is possible to have control over singularities and permits to compare the desired and generated path avoiding translation and rotation effects.

scholarly journals Levenberg-Marquardt method for absolute value equation associated with second-order cone

2022 ◽  
Vol 12 (1) ◽  
pp. 47
Author(s):  
Xin-He Miao ◽  
Kai Yao ◽  
Ching-Yu Yang ◽  
Jein-Shan Chen
Keyword(s):  
Good Choice ◽  
Second Order ◽  
Smoothing Newton Method ◽  
Numerical Comparison ◽  
Absolute Value Equation ◽  
Absolute Value ◽  
Marquardt Method ◽  
Second Order Cone ◽  
Levenberg Marquardt ◽  
Armijo Line Search

<p style='text-indent:20px;'>In this paper, we suggest the Levenberg-Marquardt method with Armijo line search for solving absolute value equations associated with the second-order cone (SOCAVE for short), which is a generalization of the standard absolute value equation frequently discussed in the literature during the past decade. We analyze the convergence of the proposed algorithm. For numerical reports, we not only show the efficiency of the proposed method, but also present numerical comparison with smoothing Newton method. It indicates that the proposed algorithm could also be a good choice for solving the SOCAVE.</p>

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