Analysis of a smoothing Newton method for second-order cone complementarity problem

2009 ◽  
Vol 31 (1-2) ◽  
pp. 459-473 ◽  
Author(s):  
Xiangsong Zhang ◽  
Sanyang Liu ◽  
Zhenhua Liu
Keyword(s):  
Newton Method ◽  
Complementarity Problem ◽  
Second Order ◽  
Smoothing Newton Method ◽  
Second Order Cone

scholarly journals A smoothing Newton method for the second-order cone complementarity problem

2013 ◽  
Vol 58 (2) ◽  
pp. 223-247 ◽  
Author(s):  
Jingyong Tang ◽  
Guoping He ◽  
Li Dong ◽  
Liang Fang ◽  
Jinchuan Zhou
Keyword(s):  
Newton Method ◽  
Complementarity Problem ◽  
Second Order ◽  
Smoothing Newton Method ◽  
Second Order Cone

scholarly journals A globally and quadratically convergent smoothing Newton method for solving second-order cone optimization

2015 ◽  
Vol 39 (8) ◽  
pp. 2180-2193 ◽  
Author(s):  
Jingyong Tang ◽  
Guoping He ◽  
Li Dong ◽  
Liang Fang ◽  
Jinchuan Zhou
Keyword(s):  
Newton Method ◽  
Second Order ◽  
Smoothing Newton Method ◽  
Second Order Cone

scholarly journals A Smoothing Method with Appropriate Parameter Control Based on Fischer-Burmeister Function for Second-Order Cone Complementarity Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Yasushi Narushima ◽  
Hideho Ogasawara ◽  
Shunsuke Hayashi
Keyword(s):  
Complementarity Problem ◽  
Quadratic Convergence ◽  
Complementarity Problems ◽  
Optimization Problems ◽  
Second Order ◽  
Smoothing Newton Method ◽  
System Of Equations ◽  
Important Class ◽  
Nonsmooth System ◽  
Second Order Cone

We deal with complementarity problems over second-order cones. The complementarity problem is an important class of problems in the real world and involves many optimization problems. The complementarity problem can be reformulated as a nonsmooth system of equations. Based on the smoothed Fischer-Burmeister function, we construct a smoothing Newton method for solving such a nonsmooth system. The proposed method controls a smoothing parameter appropriately. We show the global and quadratic convergence of the method. Finally, some numerical results are given.

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