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  • 1
    Electronic Resource
    Electronic Resource
    Linear Programming Approximations for Markov Control Processes in Metric Spaces (1998)
    Springer
    Acta applicandae mathematicae 51 (1998), S. 123-139 
    Details
    ISSN: 1572-9036
    Keywords: (discrete-time) Markov control processes ; infinite-dimensional linear programming ; aggregation ; relaxation ; inner approximations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We develop a general framework to analyze the convergence of linear-programming approximations for Markov control processes in metric spaces. The approximations are based on aggregation and relaxation of constraints, as well as inner approximations of the decision variables. In particular, conditions are given under which the control problem’s optimal value can be approximated by a sequence of finite-dimensional linear programs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005826226226
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  • 2
    Electronic Resource
    Electronic Resource
    Policy Iteration for Average Cost Markov Control Processes on Borel Spaces (1997)
    Springer
    Acta applicandae mathematicae 47 (1997), S. 125-154 
    Details
    ISSN: 1572-9036
    Keywords: (discrete-time) Markov control processes ; average cost ; policy iteration (a.k.a. Howard's algorithm)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper studies the policy iteration algorithm (PIA) for average cost Markov control processes on Borel spaces. Two classes of MCPs are considered. One of them allows some restricted-growth unbounded cost functions and compact control constraint sets; the other one requires strictly unbounded costs and the control constraint sets may be non-compact. For each of these classes, the PIA yields, under suitable assumptions, the optimal (minimum) cost, an optimal stationary control policy, and a solution to the average cost optimality equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005781013253
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