Inertial proximal point algorithm for variational inclusion in Hadamard manifolds

2021 ◽  
pp. 1-12
Author(s):  
Shih-Sen Chang ◽  
Jen-Chih Yao ◽  
M. Liu ◽  
L. C. Zhao
Keyword(s):  
Proximal Point Algorithm ◽  
Variational Inclusion ◽  
Hadamard Manifolds ◽  
Proximal Point

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."

scholarly journals A modified proximal point algorithm for solving variational inclusion problem in real Hilbert spaces

2020 ◽  
Vol 2020 (1) ◽  
pp. 28-39
Author(s):  
Thierno M. M. Sow
Keyword(s):  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Proximal Point Algorithm ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Proximal Point ◽  
Inclusion Problems ◽  
Common Solution ◽  
Variational Inclusion Problem ◽  
The Common

AbstractThe purpose of this paper is to use a modified proximal point algorithm for solving variational inclusion problem in real Hilbert spaces. It is proven that the sequence generated by the proposed iterative algorithm converges strongly to the common solution of the convex minimization and variational inclusion problems.

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