A lower bound for the mixed µ problem

The mixed µ problem has been shown to be NP hard so that exact analysis appears intractable. Our goal then is to exploit the problem structure so as to develop a polynomial time algorithm that approximates µ and usually gives good answers. To this end it is shown that µ is equivalent to a real eigenvalue maximization problem, and a power algorithm is developed to tackle this problem. The algorithm not only provides a lower bound for µ but has the property that µ is (almost) always an equilibrium point of the algorithm.