On the Convergence Rate of a Proximal Point Algorithm for Vector Function on Hadamard Manifolds  

作　　者：Feng-Mei Tang Ping-Liang Huang 

机构地区：[1]College of Science,Shanghai University,Shanghai 200444,China

出　　处：《Journal of the Operations Research Society of China》2017年第3期405-417,共13页中国运筹学会会刊（英文）

摘　　要：The proximal point algorithm has many interesting applications,such as signal recovery,signal processing and others.In recent years,the proximal point method has been extended to Riemannian manifolds.The main advantages of these extensions are that nonconvex problems in classic sense may become geodesic convex by introducing an appropriate Riemannian metric,constrained optimization problems may be seen as unconstrained ones.In this paper,we propose an inexact proximal point algorithm for geodesic convex vector function on Hadamard manifolds.Under the assumption that the objective function is coercive,the sequence generated by this algorithm converges to a Pareto critical point.When the objective function is coercive and strictly geodesic convex,the sequence generated by this algorithm converges to a Pareto optimal point.Furthermore,under the weaker growth condition,we prove that the inexact proximal point algorithm has linear/superlinear convergence rate.

关 键 词：Inexact proximal point algorithm Hadamard manifolds Convergence rate Pareto critical point Pareto optimal point 

分 类 号：O17[理学—数学]