Proximal Point Algorithm for Quasi-Convex Minimization Problems in 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: | In this paper, the proximal point algorithm for quasi-convex minimization problem in nonpositive curvature metric spaces is studied. We prove Δ-convergence of the generated sequence to a critical point (which is defined in the text) of an objective quasi-convex, proper and lower semicontinuous function with at least a minimum point as well as some strong convergence results to a minimum point with some additional conditions. The results extend the recent results of the proximal point algorithm in Hadamard manifolds and CAT(0) spaces. |
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Keywords: | Δ-convergence Hadamard space metric convergence minimization proximal point algorithm quasi-convex |
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