The number of active equality constraints exceeds the number of variables

[hongkai-dai]

Theoretically when solving an LP (except for pathalogical cases), the number of active constraints should be the same as the number of variables, and we can invert the matrix corresponding to the left-hand side of the active constraints. In our problem when computing the Lyapunov maximal violation, we often get a lot more active constraints than the number of decision variables, and the matrix to be inverted is a tall/thin matrix.

[hongkai-dai]

Many of the constraints are only on the binary variables, and we don't consider the derivative of binary variables w.r.t the problem data. We should ignore these constraints when computing the optimal continuous value solution.