Titlebook: Dynamic Optimization; Deterministic and St Karl Hinderer,Ulrich Rieder,Michael Stieglitz Textbook 2016 Springer International Publishing AG

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Einleitung: Mensch, Gehirn und Wissenschaft,Here we deal with the following questions, assuming that the functions under consideration are defined on convex sets or on a non-degenerate discrete interval.

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Offstage

,ב,In this book we prefer to place more emphasis, at least from the conceptual point of view, on . than on DP.. There are a number of reasons for our approach. We present the general theory for . and discuss the optimality equation (Bellman equation) for the limit value function. DPs with infinite horizon are also considered.

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,נ,Firstly we introduce MDPs with finite state spaces, prove the reward iteration and derive the basic solution techniques: value iteration and optimality criterion. Then MDPs with finite transition law are considered. There the set of reachable states is finite.

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,ה,In this chapter we investigate several examples and models with finite transition law: an allocation problem with random investment, an inventory problem, MDPs with an absorbing set of states, MDPs with random initial state, stopping problems and terminating MDPs. Finally, stationary MDPs are generalized to non-stationary MDPs.

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,ה,We consider MDPs with countable state spaces and variable discount factors. The discount factor may depend on the state and the action. Under minimal assumptions we prove the reward iteration and formulate a structure theorem for MDPs. Also the useful notion of a bounding function is introduced.

paradigm

,ו,In this chapter we apply the general theorems from Chap. . to special examples. In particular, we consider a production-inventory problem with backlogging and delivery lag and a queueing model with arrival control.