Applied Mathematicsematics

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By Daniel Axehill.

ISBN-10: 9185457906

ISBN-13: 9789185457908

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In the MINLP case there exist important problem classes where branch and bound is not the best method. A review of different methods of solving MIQP problems can be found in [98]. There exist several software for solving MIQP problems. m can be used. A commonly used commercial software is CPLEX. 2 Branch and Bound If computational burden is not considered, the most straightforward approach to compute the optimal solution to an optimization problem involving binary variables is to enumerate all possible combinations of the binary variables, and for each such combination, compute the optimal solution of any real variables also included in the problem.

These nodes are called leaves. One of the features of branch and bound is that the entire tree is not known from the beginning. Only the parts of the tree needed in the solution process are expanded. The optimal solution over the set S can be computed by optimizing over the smaller 28 2 Optimization sets separately according to z i∗ = minimize f0 (x), i ∈ {1, . . 47) The optimal solution over S is found as the optimal solution to the subproblem with the lowest optimal objective function value.

The resulting optimization problem is a variant of a QP, namely a Quadratically Constrained Quadratic Program (QCQP). After 40 3 Mixed Integer Predictive Control rewriting the QCQP into a Second Order Cone Program (SOCP), it is shown in [105] how Riccati recursion can be used to decrease the complexity of the calculations of the search directions in the IP algorithm. In [95, 96], the Riccati recursion is thoroughly derived and it is applied to IP LP solvers for solving MPC problems with linear objective function.

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Applications of integer quadratic programming in control and communication by Daniel Axehill.


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