Titlebook: Optimization and Approximation; Pablo Pedregal Textbook 2017 Springer International Publishing AG 2017 Linear programming.Nonlinear progra

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Numerical ApproximationAs most likely readers may have realized, it is not at all reasonable to pretend to find solutions for optimization problems, especially if they reflect a real situation, by hand.

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Numerical Approximation of Variational ProblemsWe have realized pretty soon that finding optimal solutions for optimization problems, even for moderate-sized cases, is an impossible task by hand, or in a symbolic, analytical manner. This is even more so for variational problems, and optimal control problems.

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Basic Facts About Optimal ControlJust as variational problems, optimal control problems are optimization problems where possibilities and strategies are represented by functions, and costs are expressed, most of the time, by integrals.

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Hints and Solutions to ExercisesAccording to the fundamental property of LP, it suffices to evaluate each linear function on the four vertices, and conclude on the maximum and the infimum. It is, by no means, necessary to have a full description of the feasible set, though it is not difficult (a bit tedious though) to do so.

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978-3-319-64842-2Springer International Publishing AG 2017

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Textbook 2017mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process..

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