## Linear Programming and Finite Markovian Control Problems |

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### Contents

INTRODUCTION | 1 |

MARKOV DECISION PROCESSES | 19 |

TOTAL REWARD CRITERION | 35 |

8 other sections not shown

### Common terms and phrases

a e A(i action AMD-model assumption average optimal policy average reward bias optimal policy completely ergodic completes the proof compute an optimal Consequently constraints construction contracting dynamic programming corresponding defined DENARDO denote dual linear programming dynamic programming problem ergodic set exists extreme feasible solution extreme optimal solution extreme point finite number follows go to step Hence i e E i e E\E I-P f i,j e implies infinite solution Iteration j e E lemma Let f linear programming problem Markov chain induced Markov decision problem matrix obtain oo oo Piaj Piajē policy f pure and stationary REMARK reward criterion satisfies simplex method simplex tableau solution of problem solution of program stationary average optimal stationary optimal policy stationary policy stochastic game superharmonic Suppose theorem transition probabilities val TMG variables vector