A strong convergence theorem for monotone inclusion and minimization problems in complete CAT(0) spaces

In this paper, a Halpern-type proximal point algorithm for approximating a common solution of monotone inclusion problem, minimization problem (MP) and fixed point problem is introduced. Using our algorithm, we state and prove a strong convergence theorem for approximating an element in the intersec...

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Bibliographic Details
Published in:Optimization methods & software 2019-11, Vol.34 (6), p.1168-1183
Main Authors: Okeke, C. C., Izuchukwu, C.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Convergence
fixed point problem
minimization problem
Monotone inclusion problem
monotone operators
non-expansive mappings
Optimization
resolvent operators
Theorems
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Summary:In this paper, a Halpern-type proximal point algorithm for approximating a common solution of monotone inclusion problem, minimization problem (MP) and fixed point problem is introduced. Using our algorithm, we state and prove a strong convergence theorem for approximating an element in the intersection of the set of solutions of a monotone inclusion problem, the set of solutions of an MP and the set of solutions of a fixed point problem for non-expansive mappings in complete CAT(0) spaces.
ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2018.1472259