## Linear programming and finite Markovian control problems |

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### Contents

INTRODUCTION 1 | ix |

MARKOV DECISION PROCESSES | 19 |

TOTAL REWARD CRITERION | 35 |

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### Common terms and phrases

a e A(i aeA(i 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 convex set 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 ia i e E\E i,j e ia ia implies induced by P(f iterations lemma Let f linear programming problem Markov chain induced Markov decision problem matrix obtain optimal stopping P(ir policy f policy for player pure and stationary REMARK satisfies simplex algorithm simplex method simplex tableau solution of problem solution of program stationary average optimal stationary optimal policy stationary policy step 2a stochastic game superharmonic Suppose theorem transition probabilities val(TMG variables vector x(ir