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CONVERGENCE OF THE RELATIVE VALUE ITERATION FOR THE ERGODIC CONTROL PROBLEM OF NONDEGENERATE DIFFUSIONS UNDER NEAR-MONOTONE COSTS

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Title CONVERGENCE OF THE RELATIVE VALUE ITERATION FOR THE ERGODIC CONTROL PROBLEM OF NONDEGENERATE DIFFUSIONS UNDER NEAR-MONOTONE COSTS
 
Creator ARAPOSTATHIS, A
BORKAR, VS
KUMAR, KS
 
Subject controlled diffusions
ergodic control
Hamilton-Jacobi-Bellman equation
relative value iteration
parabolic Cauchy problem
MARKOV DECISION-PROCESSES
PARABOLIC EQUATIONS
ALGORITHM
 
Description We study the relative value iteration for the ergodic control problem under a near-monotone running cost structure for a nondegenerate diffusion controlled through its drift. This algorithm takes the form of a quasi-linear parabolic Cauchy initial value problem in R-d. We show that this Cauchy problem stabilizes or, in other words, that the solution of the quasi-linear parabolic equation converges for every bounded initial condition in C-2(R-d) to the solution of the Hamilton-Jacobi-Bellman equation associated with the ergodic control problem.
 
Publisher SIAM PUBLICATIONS
 
Date 2014-12-28T11:12:23Z
2014-12-28T11:12:23Z
2014
 
Type Article
 
Identifier SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 52(1)1-31
0363-0129
1095-7138
http://dx.doi.org/10.1137/130912918
http://dspace.library.iitb.ac.in/jspui/handle/100/16327
 
Language English