2 research outputs found
Rates of convergence for inexact Krasnosel'skii-Mann iterations in Banach spaces
We study the convergence of an inexact version of the classical
Krasnosel'skii-Mann iteration for computing fixed points of nonexpansive maps.
Our main result establishes a new metric bound for the fixed-point residuals,
from which we derive their rate of convergence as well as the convergence of
the iterates towards a fixed point. The results are applied to three variants
of the basic iteration: infeasible iterations with approximate projections, the
Ishikawa iteration, and diagonal Krasnosels'kii-Mann schemes. The results are
also extended to continuous time in order to study the asymptotics of
nonautonomous evolution equations governed by nonexpansive operators
Value and Policy Iteration in Optimal Control and Adaptive Dynamic Programming
In this paper, we consider discrete-time infinite horizon problems of optimal
control to a terminal set of states. These are the problems that are often
taken as the starting point for adaptive dynamic programming. Under very
general assumptions, we establish the uniqueness of solution of Bellman's
equation, and we provide convergence results for value and policy iteration