## Duality in Stochastic Linear and Dynamic Programming |

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### Contents

INTRODUCTION AND SUMMARY | 1 |

MATHEMATICAL PROGRAMMING AND DUALITY THEORY | 9 |

STOCHASTIC LINEAR PROGRAMMING MODELS | 21 |

Copyright | |

5 other sections not shown

### Common terms and phrases

assume assumption backward recursion Borel measurable Borel sets bounding functions Chapter characterized compact convex function convex programming cost function cost-to-go functions decision defined definition demands derivatives deterministic dual dynamic programming dual pair dual problem duality theory dynamic programming dynamic programming method equivalent exists feasible solution follows formulated function f Hence holds ICCs ID(T implies inf DPA inf SDP interpreted inventory control models IP(T Lemma lower semicontinuous marginal problem Markovian maximize measurable function minimize Moreover multistage stochastic nonempty nonnegative normal integrand objective function OP(a optimal solution optimal value function optimization problem perturbations positive cones primal probability distribution probability measures proof Proposition random variables recourse models restrict risk aversion satisfies SDP2 Section solves space stochastic dynamic programming stochastic linear programming stochastic programming subset Theorem 4.5 topology vector well-defined