scholarly journals Proximal Point Algorithm for Quasi-Convex Minimization Problems in Metric Spaces

2017 ◽  
Vol 39 (4) ◽  
pp. 438-448 ◽  
Author(s):  
Hadi Khatibzadeh ◽  
Vahid Mohebbi
Keyword(s):  
Proximal Point Algorithm ◽  
Metric Spaces ◽  
Convex Minimization ◽  
Proximal Point ◽  
Minimization Problems ◽  
Convex Minimization Problems

scholarly journals On θ-generalized demimetric mappings and monotone operators in Hadamard spaces

2020 ◽  
Vol 53 (1) ◽  
pp. 95-111 ◽  
Author(s):  
Grace N. Ogwo ◽  
Chinedu Izuchukwu ◽  
Kazeem O. Aremu ◽  
Oluwatosin T. Mewomo
Keyword(s):  
Fixed Point ◽  
Proximal Point Algorithm ◽  
Monotone Operators ◽  
Finite Family ◽  
Hadamard Space ◽  
Proximal Point ◽  
Main Interest ◽  
Minimization Problems ◽  
Convex Feasibility ◽  
Convex Minimization Problems

AbstractOur main interest in this article is to introduce and study the class of θ-generalized demimetric mappings in Hadamard spaces. Also, a Halpern-type proximal point algorithm comprising this class of mappings and resolvents of monotone operators is proposed, and we prove that it converges strongly to a fixed point of a θ-generalized demimetric mapping and a common zero of a finite family of monotone operators in a Hadamard space. Furthermore, we apply the obtained results to solve a finite family of convex minimization problems, variational inequality problems and convex feasibility problems in Hadamard spaces.

scholarly journals A modified proximal point algorithm involving nearly asymptotically quasi-nonexpansive mappings

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sabiya Khatoon ◽  
Watcharaporn Cholamjiak ◽  
Izhar Uddin
Keyword(s):  
Computational Result ◽  
Proximal Point Algorithm ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Common Element ◽  
Proximal Point ◽  
Minimization Problems ◽  
Numerical Result ◽  
Convex Minimization Problems ◽  
The Common

AbstractIn this paper, we propose a modified proximal point algorithm based on the Thakur iteration process to approximate the common element of the set of solutions of convex minimization problems and the fixed points of two nearly asymptotically quasi-nonexpansive mappings in the framework of $\operatorname{CAT}(0)$ CAT ( 0 ) spaces. We also prove the Δ-convergence of the proposed algorithm. We also provide an application and numerical result based on our proposed algorithm as well as the computational result by comparing our modified iteration with previously known Sahu’s modified iteration.

scholarly journals A primal-dual dynamical approach to structured convex minimization problems

2020 ◽  
Vol 269 (12) ◽  
pp. 10717-10757 ◽  
Author(s):  
Radu Ioan Boţ ◽  
Ernö Robert Csetnek ◽  
Szilárd Csaba László
Keyword(s):  
Convex Minimization ◽  
Minimization Problems ◽  
Dynamical Approach ◽  
Convex Minimization Problems ◽  
Primal Dual
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