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By Daniel Axehill.

ISBN-10: 9185457906

ISBN-13: 9789185457908

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In the article, the results for discretized infinite-dimensional optimal control problems in [27, 28] are generalized to a general QP formulation. The dual problem to a QP is considered in several books. Some examples are [77], [43] and [10]. 5 Mixed Integer Quadratic Programming Mixed Integer Quadratic Programming (MIQP) is a special case of Mixed Integer NonLinear Programming (MINLP). 21). There is however one important difference. The optimization variables are not only allowed to be real valued, but also integer valued.

Similarly, the nodes at the bottom of the tree do not have any children. 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.

This can be explained by the fact that in the optimal solution there must not exist any violated constraints. 5 Mixed Integer Quadratic Programming 25 while maintaining the subproblems feasible, the optimization problem is not feasible. If the new subproblem is feasible, the working set is updated and the procedure is continued. A difference with this algorithm compared to [65] and [94] is that the former does not explicitly form the dual problem. The “duality” in the algorithm can be said to stem from the fact that it maintains dual feasibility instead of primal feasibility during the changes to the active set.

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


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