scholarly journals The proximal point algorithm in metric spaces

2012 ◽  
Vol 194 (2) ◽  
pp. 689-701 ◽  
Author(s):  
Miroslav Bačák
Keyword(s):  
Proximal Point Algorithm ◽  
Metric Spaces ◽  
Proximal Point

New results on the proximal point algorithm in non-positive curvature metric spaces

Optimization ◽  
2017 ◽  
Vol 66 (7) ◽  
pp. 1191-1199 ◽  
Author(s):  
Hadi Khatibzadeh ◽  
Vahid Mohebbi ◽  
Sajad Ranjbar
Keyword(s):  
Proximal Point Algorithm ◽  
Metric Spaces ◽  
Positive Curvature ◽  
Proximal Point

scholarly journals Halpern-type proximal point algorithm in complete CAT(0) metric spaces

2016 ◽  
Vol 24 (3) ◽  
pp. 141-159 ◽  
Author(s):  
Mohammad Taghi Heydari ◽  
Sajad Ranjbar
Keyword(s):  
Convergence Theorem ◽  
Proximal Point Algorithm ◽  
Metric Spaces ◽  
Proximal Point

AbstractFirst, Halpern-type proximal point algorithm is introduced in complete CAT(0) metric spaces. Then, Browder convergence theorem is considered for this algorithm and also we prove that Halpern-type proximal point algorithm converges strongly to a zero of the operator.

Proximal point algorithm involving fixed point of nonexpansive mapping in 𝑝-uniformly convex metric space

2019 ◽  
Vol 10 (4) ◽  
pp. 437-446 ◽  
Author(s):  
Godwin C. Ugwunnadi ◽  
Chinedu Izuchukwu ◽  
Oluwatosin T. Mewomo
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Metric Space ◽  
Proximal Point Algorithm ◽  
Metric Spaces ◽  
Uniformly Convex ◽  
Convex Metric Space ◽  
Proximal Point ◽  
Common Solution ◽  
Uniformly Convex Metric Space

AbstractWe prove some important properties of the p-resolvent mapping recently introduced by B. J. Choi and U. C. Ji, The proximal point algorithm in uniformly convex metric spaces, Commun. Korean Math. Soc. 31 2016, 4, 845–855, in p-uniformly convex metric space. Furthermore, we introduce a modified Mann-type PPA involving nonexpansive mapping and prove that the sequence generated by the algorithm converges to a common solution of a finite family of minimization problems, which is also a fixed point of a nonexpansive mapping in the framework of a complete p-uniformly convex metric space.

MONOTONE OPERATORS AND THE PROXIMAL POINT ALGORITHM IN COMPLETE CAT(0) METRIC SPACES

2016 ◽  
Vol 103 (1) ◽  
pp. 70-90 ◽  
Author(s):  
HADI KHATIBZADEH ◽  
SAJAD RANJBAR
Keyword(s):  
Strong Convergence ◽  
Monotone Operator ◽  
Proximal Point Algorithm ◽  
Metric Spaces ◽  
Monotone Operators ◽  
Proximal Point ◽  
Range Condition ◽  
Special Cases ◽  
Inexact Proximal

In this paper, we generalize monotone operators, their resolvents and the proximal point algorithm to complete CAT(0) spaces. We study some properties of monotone operators and their resolvents. We show that the sequence generated by the inexact proximal point algorithm $\unicode[STIX]{x1D6E5}$-converges to a zero of the monotone operator in complete CAT(0) spaces. A strong convergence (convergence in metric) result is also presented. Finally, we consider two important special cases of monotone operators and we prove that they satisfy the range condition (see Section 4 for the definition), which guarantees the existence of the sequence generated by the proximal point algorithm.

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 ◽  
◽  
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...  
Keyword(s):  
Proximal Point Algorithm ◽  
Proximal Point ◽  
Convergence Theorems
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