The Dual Simplex-Type Method for Linear Second-Order Cone Programming Problem

2020 ◽  
pp. 301-316
Author(s):  
Vitaly Zhadan
Keyword(s):  
Programming Problem ◽  
Second Order ◽  
Type Method ◽  
Cone Programming ◽  
Second Order Cone Programming ◽  
Second Order Cone ◽  
Dual Simplex

A New Smoothing Method Based on Nonsmooth FB Function for Second-Order Cone Programming

2012 ◽  
Vol 532-533 ◽  
pp. 1000-1005
Author(s):  
You Fang Zeng ◽  
Jin Bao Jian ◽  
Chun Ming Tang
Keyword(s):  
Line Search ◽  
Linear Equations ◽  
Second Order ◽  
Smoothing Function ◽  
System Of Linear Equations ◽  
Type Method ◽  
Cone Programming ◽  
Second Order Cone Programming ◽  
Second Order Cone ◽  
Starting Point

Based on a new smoothing function of the well-known nonsmooth FB (Fischer-Burmeis-ter) function, a smoothing Newton-type method for second-order cone programming problems is presented in this paper. The features of this method are following: firstly, the starting point can be chosen arbitrarily; secondly, at each iteration, only one system of linear equations and one line search are performed; finally, global, strong convergence and Q-quadratic convergent rate are obtained. The numerical results demonstrate the effectiveness of the algorithm.

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