Let At+ be the matrix composed of the positive elements of Wt in XXXXXXXXXXwith zeros elsewhere). Use this to construct a bound on any feasible dual variable   with Theorem 3 to obtain an upper bound...

Let At+ be the matrix composed of the positive elements of Wt in (5.14) (with zeros elsewhere). Use this to construct a bound on any feasible dual variable

with Theorem 3 to obtain an upper bound on the optimal objective value using the solution to the mean value problem.