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Convex Relaxations for Mixed-Integer Nonlinear Programs - Martin Ballerstein

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2013-09-16
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This thesis deals with new techniques to construct a strong convex relaxation for a mixed-integer nonlinear program (MINLP). While local optimization software can quickly identify promising operating points of MINLPs, the solution of the convex relaxation provides a global bound on the optimal value of the MINLP that can be used to evaluate the quality of the local solution. Certainly, the efficiency of thi ... Visas aprašymas

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This thesis deals with new techniques to construct a strong convex relaxation for a mixed-integer nonlinear program (MINLP). While local optimization software can quickly identify promising operating points of MINLPs, the solution of the convex relaxation provides a global bound on the optimal value of the MINLP that can be used to evaluate the quality of the local solution. Certainly, the efficiency of this evaluation is strongly dependent on the quality of the convex relaxation. Convex relaxations of general MINLPs can be constructed by replacing each nonlinear function occurring in the model description by convex underestimating and concave overestimating functions. In this setting, it is desired to use the best possible convex underestimator and concave overestimator of a given function over an underlying domain ¿ the so-called convex and concave envelope, respectively. However, the computation of these envelopes can be extremely difficult so that analytical expressions for envelopes are only available for some classes of well-structured functions.

Daugiau informacijos

Autorius Martin Ballerstein
Leidėjas Cuvillier
Išleidimo metai 2013
Viršelio tipas Minkšti viršeliai
EAN 9783954044740
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47,34 € 63,12 €