By Daniel Axehill.
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Das Buch vermittelt einen umfassenden ? berblick ? ber Modelle und Algorithmen zur dynamischen Losgr? ?enoptimierung f? r ein- und mehrstufige Erzeugnisstrukturen, die eingehend erl? utert und anhand zahlreicher Beispiele veranschaulicht werden. Au? erdem werden Verfahren zur optimalen Bestellmengenplanung und Lieferantenauswahl unter Beachtung von Mengenrabatten dargestellt.
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37) where A ∈ Rm×n has full row rank, that is rank A = m. If A does not have full row rank, the constraints are either inconsistent or some constraints are redundant in which case they can be deleted without changing the solution to the problem. Using the equation Ax = b, m variables can be eliminated from the problem by expressing them in the other n − m remaining variables. Choose matrices Y ∈ Rn×m and Z ∈ Rn×(n−m) such that Y Z is nonsingular. Further, Z and Y should fulfill AY = I and AZ = 0.
After the optimization has been performed, only the first control signal in the optimal control signal sequence computed is applied to the system and the others are ignored. In the next time step, a new optimization is performed and the procedure is repeated. Due to modeling errors and unknown disturbances, the predicted behavior and the actual behavior of the system do not usually completely coincide. Such errors are, if they are sufficiently small, handled by the feedback in the algorithm. 1.
In the reference, both the method presented in  and the method presented in  are compared to the algorithm. According to , the algorithm presented in the cited reference is more efficient and more numerically stable than . A drawback with the dual algorithm is also mentioned. If the Hessian is ill-conditioned, numerical problems might occur since the dual algorithm starts from the unconstrained optimum. The numerical properties of the algorithm presented in  are further examined in , where an extension to handle ill-conditioned problems is presented and the algorithm is compared to two primal QP solvers QPSOL and VEO2A.
Applications of integer quadratic programming in control and communication by Daniel Axehill.