Читать книгу Multi-parametric Optimization and Control - Efstratios N. Pistikopoulos - Страница 59

Consider . Then an optimal solution of the resulting LP problem is guaranteed to lie in a vertex, thus featuring active constraints. However, as the equality constraints have to be fulfilled for all , the number of active inequality constraints is given by , where is the number of equality constraints. As the number of critical regions is uniquely defined by the active set, it is bound by above by all possible combinations of active sets, which is given by , which completes the proof.