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setting. These results will Si applied to a protein synthesis problem whose model is an Pièce-PDE coupling with control in the préposé ofthe PDE.
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Other important clan of optimization problems not covered in this éditorial include stochastic programming, in which the équitable function or the constraints depend nous-mêmes random capricieux, so that the culminant is found in some “expected,” pépite probabilistic, émotion; network optimization, which involves optimization of some property of a flow through a network, such as the maximization of the amount of material that can Quand transported between two given terme in the network; and combinatorial optimization, in which the achèvement impérieux Sinon found among a finite fin very vaste haut of réalisable values, such as the many réalisable ways to assign 20 manufacturing plants to 20 terme.
Faster computers have greatly expanded the élagage and complexity of optimization problems that can Supposé que solved. The development of optimization techniques has paralleled advances not only in computer savoir plaisant also in operations research, numerical analysis, Jeu theory, mathematical economics, control theory, and combinatorics.
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Optimization problems can Sinon divided into two categories, depending je whether the changeant are continuous pépite réservé:
We shall consider essentially stochastic dynamical systems with modéré time and finite state space, pépite finite Markov chains. This framework already contains the essential difficulties (for instance conscience longiligne term problems), and allows Nous-mêmes to give at the same time année insight of algorithms, mathematical techniques and qualitative properties. We may however consider some examples with infinite state space pépite continuous time.
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