Читать книгу Multi-parametric Optimization and Control - Efstratios N. Pistikopoulos - Страница 67

Primal degeneracy is caused by the presence of weakly redundant constraints, i.e. constraints that are redundant yet intersect with the feasible parameter space (see Chapter 1.3). In particular, the space where the weakly redundant constraints hold as equality is lower‐dimensional with respect to the overall feasible parameter space. Thus, it is clear that if any weakly redundant constraint is chosen as an element of the active set, then the resulting critical region will be lower‐dimensional.4 As a consequence, from all possible combinations of active sets at a given solution, only one active set exists, which results in a full‐dimensional critical region, which does not feature any weakly redundant constraints. In the case of Figure 2.4, . Note that the presence of a lower‐dimensional critical region can be detected by calculating the radius of the Chebyshev ball (see Chapter 1.3).