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

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Introduction and Organization of the Book,In this treatise we deal with optimization problems whose objective functions show a sequential structure and hence are amenable to sequential methods. The corresponding field mostly goes by the name .. Other names are . and .. In order to avoid possible confusion with programming in computer science we speak of ..

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Examples of Deterministic Dynamic ProgramsIn this chapter we explicitly solve the following: optimal routing of a freighter, a production-inventory problem with linear costs, allocation and linear-quadratic problems and a scheduling problem. Then we discuss some further models: DPs with random length of periods and with random termination.

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Absorbing Dynamic Programs and Acyclic NetworksWe study the problem of maximizing the sum of discounted rewards, earned not over a fixed number of periods, but until the decision process enters a given absorbing set. The basic theorem for absorbing DPs is derived. Moreover, we show how absorbing DPs can be used to find cost-minimal subpaths in acyclic networks.

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Concavity and Convexity of the Value FunctionsHere 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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Control Models with DisturbancesIn this chapter we introduce control models with finite and i.i.d. disturbances. We prove the reward iteration and derive the basic solution techniques: value iteration and optimality criterion.

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Markovian Decision Processes with Finite Transition LawFirstly 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.