A globally convergent non-interior point homotopy method for solving variational inequalities

2011 ◽  
Vol 26 (6) ◽  
pp. 933-943
Author(s):  
Yufeng Shang ◽  
Qing Xu ◽  
Bo Yu
Keyword(s):  
Variational Inequalities ◽  
Interior Point ◽  
Homotopy Method ◽  
Globally Convergent

scholarly journals An Improved Two-Step Method for Generalized Variational Inequalities

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Haibin Chen
Keyword(s):  
Variational Inequalities ◽  
Error Bound ◽  
Point Of View ◽  
Large Decrease ◽  
Step Method ◽  
Generalized Variational Inequalities ◽  
Mild Conditions ◽  
Extragradient Algorithm ◽  
Globally Convergent ◽  
Geometric Point

We propose an improved two-step extragradient algorithm for pseudomonotone generalized variational inequalities. It requires two projections at each iteration and allows one to take different stepsize rules. Moreover, from a geometric point of view, it is shown that the new method has a long stepsize, and it guarantees that the distance from the next iterative point to the solution set has a large decrease. Under mild conditions, we show that the method is globally convergent, and then the R-linearly convergent property of the method is proven if a projection-type error bound holds locally.

scholarly journals A globally convergent primal-dual interior-point filter method for nonlinear programming

2004 ◽  
Vol 100 (2) ◽  
pp. 379-410 ◽  
Author(s):  
Michael Ulbrich ◽  
Stefan Ulbrich ◽  
Lu�s N. Vicente
Keyword(s):  
Nonlinear Programming ◽  
Interior Point ◽  
Filter Method ◽  
Globally Convergent ◽  
Primal Dual
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