New results on the proximal point algorithm in non-positive curvature metric spaces |
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Authors: | Hadi Khatibzadeh Vahid Mohebbi |
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Institution: | Department of Mathematics, University of Zanjan, Zanjan, Iran. |
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Abstract: | The subject of this paper is the inexact proximal point algorithm of usual and Halpern type in non-positive curvature metric spaces. We study the convergence of the sequences given by the inexact proximal point algorithm with non-summable errors. We also prove the strong convergence of the Halpern proximal point algorithm to a minimum point of the convex function. The results extend several results in Hilbert spaces, Hadamard manifolds and non-positive curvature metric spaces. |
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Keywords: | Convex minimization proximal point algorithm Halpern method Hadamard space resolvent |
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