A proximal point method for nonsmooth convex optimizationproblems in Banach spaces
Copyright policy )A proximal point method for nonsmooth convex optimizationproblems in Banach spaces
In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric characteristic of the dual Banach space, namely its modulus of convexity. We apply a new technique which includes Banach space geometry, estimates of duality mappings, nonstandard Lyapunov functionals and generalized projection operators in Banach spaces.
Convex programming, Economics, moduli of convexity and smoothness of Banach spaces, Fixed-Point Problems, Biochemistry, Gene, 90C25, convergence rate, Convexity, 49D45, Fixed Point Theorems in Metric Spaces, Interior-Point Methods, Nonexpansive Mappings, Approximation property, Interpolation space, Numerical Analysis, Numerical Optimization Techniques, Iterative Algorithms for Nonlinear Operators and Optimization, Lyapunov functionals, Convex optimization, Regular polygon, Banach spaces, Chemistry, Computational Theory and Mathematics, nonsmooth and convex functionals, Banach manifold, Physical Sciences, smooth Banach spaces, subdifferentials, Financial economics, Convex Optimization, Best Proximity Points, Geometry, estimates of convergence rate, generalized projection operators, Mathematical analysis, Reflexive space, FOS: Mathematics, constrained convex optimization, duality mappings, convergence, Banach space, Functional analysis, Applications of functional analysis in optimization, convex analysis, mathematical programming, economics, modulus of convexity, Pure mathematics, stability, Uniformly convex space, Applied mathematics, proximal point method, Convex analysis, Duality (order theory), Computer Science, Proximal point algorithm, weak convergence, Geometry and Topology, Lp space, Mathematics, 49D37
Convex programming, Economics, moduli of convexity and smoothness of Banach spaces, Fixed-Point Problems, Biochemistry, Gene, 90C25, convergence rate, Convexity, 49D45, Fixed Point Theorems in Metric Spaces, Interior-Point Methods, Nonexpansive Mappings, Approximation property, Interpolation space, Numerical Analysis, Numerical Optimization Techniques, Iterative Algorithms for Nonlinear Operators and Optimization, Lyapunov functionals, Convex optimization, Regular polygon, Banach spaces, Chemistry, Computational Theory and Mathematics, nonsmooth and convex functionals, Banach manifold, Physical Sciences, smooth Banach spaces, subdifferentials, Financial economics, Convex Optimization, Best Proximity Points, Geometry, estimates of convergence rate, generalized projection operators, Mathematical analysis, Reflexive space, FOS: Mathematics, constrained convex optimization, duality mappings, convergence, Banach space, Functional analysis, Applications of functional analysis in optimization, convex analysis, mathematical programming, economics, modulus of convexity, Pure mathematics, stability, Uniformly convex space, Applied mathematics, proximal point method, Convex analysis, Duality (order theory), Computer Science, Proximal point algorithm, weak convergence, Geometry and Topology, Lp space, Mathematics, 49D37
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).23 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!