monotone vector fields
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scholarly journals An extragradient-type algorithm for variational inequality on Hadamard manifolds

2020 ◽  
Vol 26 ◽  
pp. 63 ◽  
Author(s):  
E.E.A. Batista ◽  
G.C. Bento ◽  
O.P. Ferreira
Keyword(s):  
Variational Inequality ◽  
Vector Field ◽  
Vector Fields ◽  
Extragradient Method ◽  
Maximal Monotone ◽  
Hadamard Manifolds ◽  
Convergence Properties ◽  
Type Algorithm ◽  
Monotone Vector Fields ◽  
Maximal Monotone Vector Fields

This paper presents an extragradient method for variational inequality associated with a point-to-set vector field in Hadamard manifolds, and a study of its convergence properties. To present our method, the concept of ϵ-enlargement of maximal monotone vector fields is used, and its lower-semicontinuity is established to obtain the method convergence in this new context.

scholarly journals Metric selfduality and monotone vector fields on manifolds

2016 ◽  
Vol 271 (6) ◽  
pp. 1652-1690 ◽  
Author(s):  
Nassif Ghoussoub ◽  
Abbas Moameni
Keyword(s):  
Vector Fields ◽  
Monotone Vector Fields

Non-existence of strictly monotone vector fields on certain Riemannian manifolds

2015 ◽  
Vol 146 (1) ◽  
pp. 240-246 ◽  
Author(s):  
J. X. Cruz Neto ◽  
I. D. Melo ◽  
P. A. Sousa
Keyword(s):  
Riemannian Manifolds ◽  
Vector Fields ◽  
Monotone Vector Fields

scholarly journals Homogenization of Maximal Monotone Vector Fields via Selfdual Variational Calculus

2011 ◽  
Vol 11 (2) ◽  
Author(s):  
Nassif Ghoussoub ◽  
Abbas Moameni ◽  
Ramón Zárate Sáiz
Keyword(s):  
Vector Fields ◽  
Maximal Monotone ◽  
Variational Calculus ◽  
Classical Case ◽  
Divergence Form ◽  
Graph Convergence ◽  
Monotone Vector Fields ◽  
Γ Convergence ◽  
Maximal Monotone Vector Fields ◽  
Periodic Family

AbstractWe use the theory of selfdual Lagrangians to give a variational approach to the homogenization of equations in divergence form, that are driven by a periodic family of maximal monotone vector fields. The approach has the advantage of using Γ-convergence methods for corresponding functionals just as in the classical case of convex potentials, as opposed to the graph convergence methods used in the absence of potentials. A new variational formulation for the homogenized equation is also given.

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