scholarly journals Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities

1998 ◽  
Vol 67 (222) ◽  
pp. 519-541 ◽  
Author(s):  
X. Chen ◽  
L. Qi ◽  
D. Sun
Keyword(s):  
Variational Inequalities ◽  
Newton Method ◽  
Superlinear Convergence ◽  
Smoothing Newton Method ◽  
Global And Superlinear Convergence

scholarly journals PREDICTOR–CORRECTOR SMOOTHING NEWTON METHOD FOR SOLVING SEMIDEFINITE PROGRAMMING

2009 ◽  
Vol 79 (3) ◽  
pp. 367-376
Author(s):  
CAIYING WU ◽  
GUOQING CHEN
Keyword(s):  
Global Convergence ◽  
Semidefinite Programming ◽  
Optimality Conditions ◽  
Newton Method ◽  
Superlinear Convergence ◽  
Smoothing Newton Method ◽  
Equivalent Transformation ◽  
Newton Algorithm ◽  
Smoothing Methods ◽  
Predictor Corrector

AbstractThere has been much interest recently in smoothing methods for solving semidefinite programming (SDP). In this paper, based on the equivalent transformation for the optimality conditions of SDP, we present a predictor–corrector smoothing Newton algorithm for SDP. Issues such as the existence of Newton directions, boundedness of iterates, global convergence, and local superlinear convergence of our algorithm are studied under suitable assumptions.

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.

Sign in / Sign up

Export Citation Format

Share Document