Unified smoothing functions for absolute value equation associated with second-order cone

2019 ◽  
Vol 135 ◽  
pp. 206-227 ◽  
Author(s):  
Chieu Thanh Nguyen ◽  
B. Saheya ◽  
Yu-Lin Chang ◽  
Jein-Shan Chen
Keyword(s):  
Second Order ◽  
Absolute Value Equation ◽  
Absolute Value ◽  
Second Order Cone ◽  
Smoothing Functions

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>

Smoothing Functions for Second-Order-Cone Complementarity Problems

2002 ◽  
Vol 12 (2) ◽  
pp. 436-460 ◽  
Author(s):  
Masao Fukushima ◽  
Zhi-Quan Luo ◽  
Paul Tseng
Keyword(s):  
Complementarity Problems ◽  
Second Order ◽  
Second Order Cone ◽  
Smoothing Functions

scholarly journals The Jacobian Consistency of a One-Parametric Class of Smoothing Functions for SOCCP

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaoni Chi ◽  
Zhongping Wan ◽  
Zijun Hao
Keyword(s):  
Directional Derivative ◽  
Second Order ◽  
Smoothing Function ◽  
Smoothing Methods ◽  
Second Order Cone ◽  
Complementarity Functions ◽  
Computable Formula ◽  
Smoothing Functions ◽  
The One ◽  
Parametric Class

Second-order cone (SOC) complementarity functions and their smoothing functions have been much studied in the solution of second-order cone complementarity problems (SOCCP). In this paper, we study the directional derivative and B-subdifferential of the one-parametric class of SOC complementarity functions, propose its smoothing function, and derive the computable formula for the Jacobian of the smoothing function. Based on these results, we prove the Jacobian consistency of the one-parametric class of smoothing functions, which will play an important role for achieving the rapid convergence of smoothing methods. Moreover, we estimate the distance between the subgradient of the one-parametric class of the SOC complementarity functions and the gradient of its smoothing function, which will help to adjust a parameter appropriately in smoothing methods.

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