Entropy Minimization with Lattice Bounds Original Research Article

We characterize solutions to the problem of minimizing a convex integral objective function subject to a finite number of linear constraints and requiring that the feasible functions lie in a strip [α,β] where α and β are extended real valued measurable functions. We use the duality theory of J. M. Borwein and A. S. Lewis (Math. Programming, Series B57 (1992), 15-48, 49-84) to show that the solutions are of the usual form, but truncated where they leave the strip.