A Smoothing Newton Method for Absolute Value Equation

2016 ◽  
Vol 9 (2) ◽  
pp. 119-132 ◽  
Author(s):  
Longquan Yong
Keyword(s):  
Newton Method ◽  
Smoothing Newton Method ◽  
Absolute Value Equation ◽  
Absolute Value

A Smoothing Newton Method for Solving Absolute Value Equations

2013 ◽  
Vol 765-767 ◽  
pp. 703-708 ◽  
Author(s):  
Xiao Qin Jiang
Keyword(s):  
Newton Method ◽  
Numerical Results ◽  
Smoothing Newton Method ◽  
Absolute Value Equations ◽  
Absolute Value

In this paper, we reformulate the system of absolute value equations as afamily of parameterized smooth equations and propose a smoothing Newton method tosolve this class of problems. we prove that the method is globally and locally quadraticallyconvergent under suitable assumptions. The preliminary numerical results demonstratethat the method is effective.

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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