On the Local Convergence of Semismooth Newton Methods for Linear and Nonlinear Second-Order Cone Programs Without Strict Complementarity

2009 ◽  
Vol 20 (1) ◽  
pp. 297-320 ◽  
Author(s):  
Christian Kanzow ◽  
Izabella Ferenczi ◽  
Masao Fukushima
Keyword(s):  
Local Convergence ◽  
Second Order ◽  
Newton Methods ◽  
Strict Complementarity ◽  
Second Order Cone ◽  
Semismooth Newton ◽  
Semismooth Newton Methods ◽  
Linear And Nonlinear

scholarly journals A semismooth Newton method with analytical path-following for the $H^1$-projection onto the Gibbs simplex

2018 ◽  
Vol 39 (3) ◽  
pp. 1276-1295 ◽  
Author(s):  
L Adam ◽  
M Hintermüller ◽  
T M Surowiec
Keyword(s):  
Regularization Parameter ◽  
Image Inpainting ◽  
Path Following ◽  
Second Order ◽  
Semismooth Newton Method ◽  
Semismooth Newton ◽  
Yosida Regularization ◽  
Semismooth Newton Methods ◽  
Independent Behavior ◽  
The Value Function

Abstract An efficient, function-space-based second-order method for the $H^1$-projection onto the Gibbs simplex is presented. The method makes use of the theory of semismooth Newton methods in function spaces as well as Moreau–Yosida regularization and techniques from parametric optimization. A path-following technique is considered for the regularization parameter updates. A rigorous first- and second-order sensitivity analysis of the value function for the regularized problem is provided to justify the update scheme. The viability of the algorithm is then demonstrated for two applications found in the literature: binary image inpainting and labeled data classification. In both cases, the algorithm exhibits mesh-independent behavior.

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