CAT(0)空间混合非扩张映射修正临近点算法的收敛性（英文）
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摘要
提出了一种修正的临近点算法,来寻找单值非扩张映射、集值非扩张映射不动点点集以及凸下半连续泛函极小元集的公共元,获得了所提出算法的收敛性。
In this paper,we propose a modied proximal point algorithm for finding a common element of the set of fixed points of a single-valued nonexpansive mapping,the set of fixed points of a multivalued nonexpansive mapping,and the set of minimizers of convex and lower semicontinuous functions.We obtain the strong convergence to a common element of three sets in CAT( 0) spaces.
In this paper,we propose a modied proximal point algorithm for finding a common element of the set of fixed points of a single-valued nonexpansive mapping,the set of fixed points of a multivalued nonexpansive mapping,and the set of minimizers of convex and lower semicontinuous functions.We obtain the strong convergence to a common element of three sets in CAT( 0) spaces.
引文
[1]Bridson M,Haefliger A.Metric Spaces of Non-Positive Curvature[M].Springer,Berlin.1999.
[2]Bruhat F,Tits J.Groupes reductifs sur un corps local[M].Inst.Hautes Etudes Sci.Publ.Math.1972,41:51.
[3]Dhompongsa S,Panyanak B.On-convergence theorems in CAT(0)spaces[J].Comput.Math.Appl.2008,6:2572-2579.
[4]Martinet B.Regularisation dinquations variationnelles par approximations successives[J].Rev.Fr.Inform.Rech.Oper.1970,4:154-158.
[5]Bacak M.The proximal point algorithm in metric spaces[J].Isr.J.Math.2013,194:689-701.
[6]Guler O.On the convergence of the proximal point algorithm for convex minimization[J].SIAM J.Control Optim.1991,29:403-419.
[7]Ariza-Ruiz,D Leustean L,Lopez G.Firmly nonexpansive mappings in classes of geodesic spaces[J].Trans.Am.Math.Soc.2014,366,4299-4322.
[8]Jost J.Convex functionals and generalized harmonic maps into spaces of nonpositive curvature[J].Comment.Math.Helv.1995:659-673.
[9]Suthep Suantai.Withum Phuengrattana Proximal Point Algorithms for a Hybrid Pair of Nonexpansive Single-Valued and MultiValued Mappings in Geodesic Metric Spaces[J].2017:62.
[10]Tyrrell Rockafellar R,Wets R J B.Variational A-nalysis[M].Springer,Berlin.2005.
[11]Ambrosio L,Gigli N,Savare G.Gradient Flows in Metric Spaces and in the Space of Probability Measures[M].Lectures in Mathematics ETHZrich,2nd edn.Birkhuser,Basel.2008.
[2]Bruhat F,Tits J.Groupes reductifs sur un corps local[M].Inst.Hautes Etudes Sci.Publ.Math.1972,41:51.
[3]Dhompongsa S,Panyanak B.On-convergence theorems in CAT(0)spaces[J].Comput.Math.Appl.2008,6:2572-2579.
[4]Martinet B.Regularisation dinquations variationnelles par approximations successives[J].Rev.Fr.Inform.Rech.Oper.1970,4:154-158.
[5]Bacak M.The proximal point algorithm in metric spaces[J].Isr.J.Math.2013,194:689-701.
[6]Guler O.On the convergence of the proximal point algorithm for convex minimization[J].SIAM J.Control Optim.1991,29:403-419.
[7]Ariza-Ruiz,D Leustean L,Lopez G.Firmly nonexpansive mappings in classes of geodesic spaces[J].Trans.Am.Math.Soc.2014,366,4299-4322.
[8]Jost J.Convex functionals and generalized harmonic maps into spaces of nonpositive curvature[J].Comment.Math.Helv.1995:659-673.
[9]Suthep Suantai.Withum Phuengrattana Proximal Point Algorithms for a Hybrid Pair of Nonexpansive Single-Valued and MultiValued Mappings in Geodesic Metric Spaces[J].2017:62.
[10]Tyrrell Rockafellar R,Wets R J B.Variational A-nalysis[M].Springer,Berlin.2005.
[11]Ambrosio L,Gigli N,Savare G.Gradient Flows in Metric Spaces and in the Space of Probability Measures[M].Lectures in Mathematics ETHZrich,2nd edn.Birkhuser,Basel.2008.