Monotone vector fields and the proximal point algorithm on Hadamard manifolds

2009 ◽  
Vol 79 (3) ◽  
pp. 663-683 ◽  
Author(s):  
Chong Li ◽  
Genaro López ◽  
Victoria Martín-Márquez
Keyword(s):  
Proximal Point Algorithm ◽  
Vector Fields ◽  
Hadamard Manifolds ◽  
Proximal Point ◽  
Monotone Vector Fields

scholarly journals Existence results and two step proximal point algorithm for equilibrium problems on Hadamard manifolds

2021 ◽  
Vol 37 (3) ◽  
pp. 393-406
Author(s):  
SULIMAN AL-HOMIDAN ◽  
◽  
QAMRUL HASAN ANSARI ◽  
MONIRUL ISLAM ◽  
◽  
...  
Keyword(s):  
Proximal Point Algorithm ◽  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Coercivity Conditions ◽  
Hadamard Manifolds ◽  
Type Condition ◽  
Proximal Point ◽  
Strong Pseudomonotonicity

"In this paper, we study the existence of solutions of equilibrium problems in the setting of Hadamard manifolds under the pseudomonotonicity and geodesic upper sign continuity of the equilibrium bifunction and under different kinds of coercivity conditions. We also study the existence of solutions of the equilibrium problems under properly quasimonotonicity of the equilibrium bifunction. We propose a two-step proximal point algorithm for solving equilibrium problems in the setting of Hadamard manifolds. The convergence of the proposed algorithm is studied under the strong pseudomonotonicity and Lipschitz-type condition. The results of this paper either extend or generalize several known results in the literature."

Resolvents of Set-Valued Monotone Vector Fields in Hadamard Manifolds

2010 ◽  
Vol 19 (3) ◽  
pp. 361-383 ◽  
Author(s):  
Chong Li ◽  
Genaro López ◽  
Victoria Martín-Márquez ◽  
Jin-Hua Wang
Keyword(s):  
Vector Fields ◽  
Hadamard Manifolds ◽  
Monotone Vector Fields
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