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26 3 Methods for Energy System Modeling concurrent constraints on prices and volumes are possible under the system of equations approach, whereas such constraints may lead to infeasibility under a mathematical program setup. (cf. B¨ ohringer, 1996, pp. ). Apart from technical constraints, the choice between a system of equation versus mathematical program approach depends on the questions to be answered. e. expressing what should be be done. In contrast, solutions from systems of equations are typically descriptive, expressing what could happen.

T (ω) is called technology matrix, h(ω) is the constraining resource. Recourse matrix W is a constant. 40 3 Methods for Energy System Modeling In case the number of possible events ω is finite, the program from above can also be transformed into an extensive form (cf. Birge and Louveaux, 1997, p. 8). In this form, the decision variables for the second stage are explicitly described for all possible realizations of ω. Such an approach is followed for the stochastic models in this book, as there is a maximum of four possible states of the world in a particular stage.

N}. These conditions are necessary for a minimum of a nonlinear mathematical program with inequality constraints. The solution process based on KKT conditions is one of trial-and-error. Starting point is the assumption that one or more constraints are not binding at the extremum, implying that the associated Lagrangian multiplier λi will be zero. By requirement of complementary slackness, the inequality11 corresponding to this variable can be transformed into an equality. Moreover, often guesses on whether particular decision variables xj will be positive or zero can be made.

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ABC Buch und Lese und Denk-Uebungen bei dem ersten Unterricht der Kinder : nach den besten Mustern von Pestalozzi, Stephani und andern bearbeitet. 1. Buch


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