Regularization of proximal point algorithms in Hadamard manifolds
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In this paper, we consider the regularization method for exact as well as for inexact proximal point algorithms for finding the singularities of maximal monotone set-valued vector fields. We prove that the sequences generated by these algorithms converge to an element of the set of singularities of a maximal monotone set-valued vector field. A numerical example is provided to illustrate the inexact proximal point algorithm with regularization. Applications of our results to minimization problems and saddle point problems are given in the setting of Hadamard manifolds.
KeywordsInclusion problems regularization method proximal point algorithms maximal monotone vector fields minimization problems saddle point problems Hadamard manifolds
Mathematics Subject Classification49J53 49J40 47H05 47J22
The authors are grateful to the reviewers for their valuable suggestions and corrections that improved the first draft of this paper. In this research, the first author was supported by a research Grant of DST-SERB No. EMR/2016/005124, and the last author was supported by a research Grant No. MOST 105-2115-M-039-002-MY3.
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