New Augmented Lagrangian-Based Proximal Point Algorithm for Convex Optimization with Equality Constraints

2016 ◽  
Vol 171 (1) ◽  
pp. 251-261 ◽  
Author(s):  
Yuan Shen ◽  
Hongyong Wang
Keyword(s):  
Convex Optimization ◽  
Proximal Point Algorithm ◽  
Augmented Lagrangian ◽  
Equality Constraints ◽  
Proximal Point

scholarly journals A parameterized proximal point algorithm for separable convex optimization

2017 ◽  
Vol 12 (7) ◽  
pp. 1589-1608 ◽  
Author(s):  
Jianchao Bai ◽  
Hongchao Zhang ◽  
Jicheng Li
Keyword(s):  
Convex Optimization ◽  
Proximal Point Algorithm ◽  
Proximal Point ◽  
Separable Convex Optimization

scholarly journals Proximal point algorithms involving fixed point iteration for nonexpansive mappings in CAT(κ) spaces

2018 ◽  
Vol 34 (2) ◽  
pp. 229-237
Author(s):  
NUTTAPOL PAKKARANANG ◽  
◽  
POOM KUMAM ◽  
PRASIT CHOLAMJIAK ◽  
RAWEEROTE SUPARATULATORN ◽  
...  
Keyword(s):  
Fixed Point ◽  
Convex Optimization ◽  
Iterative Algorithm ◽  
Proximal Point Algorithm ◽  
Nonexpansive Mappings ◽  
Proximal Point ◽  
Fixed Point Iteration ◽  
Proximal Point Algorithms ◽  
Common Solution ◽  
Mild Conditions

In this paper, we propose a new modified proximal point algorithm involving fixed point iteration for nonexpansive mappings in CAT(1) spaces. Under some mild conditions, we prove that the sequence generated by our iterative algorithm ∆-converges to a common solution between certain convex optimization and fixed point problems.

STRONG AND Δ - CONVERGENCE THEOREMS USING MODIFIED PROXIMAL POINT ALGORITHM IN CAT(0) SPACES

2018 ◽  
Vol 7 (2) ◽  
pp. 8
Author(s):  
KUMAR DAS APURVA ◽  
DHAR DIWAN SHAILESH ◽  
DASHPUTRE SAMIR ◽  
◽  
◽  
...  
Keyword(s):  
Proximal Point Algorithm ◽  
Proximal Point ◽  
Convergence Theorems
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