Dynamic Construction of Approximate Subdifferentials: Dual Form of Bundle Methods

1993 ◽  
pp. 223-274
Author(s):  
Jean-Baptiste Hiriart-Urruty ◽  
Claude Lemaréchal
Keyword(s):  
Bundle Methods ◽  
Dual Form

Dynamics of a Contact Structure Along a Vector Field of its Kernel

2008 ◽  
Vol 8 (1) ◽  
Author(s):  
Abbas Bahri ◽  
Yongzhong Xu
Keyword(s):  
Vector Field ◽  
Variational Problem ◽  
Contact Structure ◽  
Contact Form ◽  
Dual Form

AbstractIn this paper we prove that in order to define the homology of [3], the hypothesis that there exists a vector field in the kernel of the contact form which defines a dual form with the same orientation is not essential. The technique is quantitative: as we introduce a large amount of rotation near the zeroes of the vector field in the kernel, we track down the modification of the variational problem and provide bounds on a key quantity (denoted by τ).

scholarly journals Asynchronous level bundle methods

2019 ◽  
Vol 184 (1-2) ◽  
pp. 319-348 ◽  
Author(s):  
Franck Iutzeler ◽  
Jérôme Malick ◽  
Welington de Oliveira
Keyword(s):  
Bundle Methods
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