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We introduce the proximal point algorithm in a $p$-uniformly convex metric space. We first introduce the notion of $p$-resolvent map in a $p$-uniformly convex metric space as a generalization of the Moreau-Yosida resolvent in a CAT($0$)-space, and then we secondly prove the convergence of the proximal point algorithm by the $p$-resolvent map in a $p$-uniformly convex metric space.
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참고문헌 (23)
참고문헌 신청
M. Bacak / 2013 / The proximal point algorithm in metric spaces / Israel J. Math 194(2):689~701
I. Beg / 2001 / Inequalities in metric spaces with applications / Topol. Methods Nonlinear Anal 17(1):183~190
B. J. Choi / 2015 / Asymptotic property for inductive means in uniformly convex metric spaces
J. A. Clarkson / 1936 / Uniformly convex spaces / Trans. Amer. Math. Soc 40(3):396~414
C. Conde / 2008 / Geometric interpolation in p-Schatten class / J. Math. Anal. Appl 340(2):920~931
I. Beg / 2001 / Inequalities in metric spaces with applications / Topol. Methods Nonlinear Anal 17(1):183~190
B. J. Choi / 2015 / Asymptotic property for inductive means in uniformly convex metric spaces
J. A. Clarkson / 1936 / Uniformly convex spaces / Trans. Amer. Math. Soc 40(3):396~414
C. Conde / 2008 / Geometric interpolation in p-Schatten class / J. Math. Anal. Appl 340(2):920~931
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