By Daniel Axehill.
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Additional info for Applications of integer quadratic programming in control and communication
This set is called the working set and is in iteration k denoted Wk . 37), where the constraints are those being indexed by A(x∗ ). If an active set solver is supplied with an initial working set W0 , which does not differ much from A(x∗ ), the problem can often be quickly solved. This idea is used in so-called warm starts, where information from a previous optimal solution is used to quickly reoptimize after a minor change to the problem. Unfortunately, A(x∗ ) is in general not known in advance.
3) and the initial constraint x(t0 ) = x0 . 3: Apply the first element u(t0 ) in u to the controlled process. 4: Set t0 := t0 + 1 and repeat the procedure. The notation and the derivations of the formulations can be found in Appendix B. 5) gives a dense optimization problem with N m variables. In order to get closed-loop control, the approach above is used in a receding horizon fashion, which means that the prediction interval is moved one step forward after each completed optimization. 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.
A difference with this algorithm compared to  and  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. The algorithm usually starts in the unconstrained primal optimum and is generally able to take advantage of a good initial estimate of the solution, . The algorithm is equivalent to a primal algorithm applied to the dual problem, [43, 48].
Applications of integer quadratic programming in control and communication by Daniel Axehill.