  This paper presents a method to certify the computational complexity of a
standard Branch and Bound method for solving Mixed-Integer Quadratic
Programming (MIQP) problems defined as instances of a multi-parametric MIQP.
Beyond previous work, not only the size of the binary search tree is
considered, but also the exact complexity of solving the relaxations in the
nodes by using recent result from exact complexity certification of active-set
QP methods. With the algorithm proposed in this paper, a total worst-case
number of QP iterations to be performed in order to solve the MIQP problem can
be determined as a function of the parameter in the problem. An important
application of the proposed method is Model Predictive Control for hybrid
systems, that can be formulated as an MIQP that has to be solved in real-time.
The usefulness of the proposed method is successfully illustrated in numerical
examples.
