Ordered Solutions for Dynamic Programs
William S. Lovejoy · Mathematics of Operations Research · 1987
Suppose X indexes a collection of optimization problems in R n and δ*(x) is an optimal program for the problem indexed by x ∈ X. Sufficient conditions are presented for two other families of optimization problems to possess optimal programs δ 0 (x) and δ 0 (x) (for the respective problems when x ∈ X) such that δ 0 (x) ≤ δ*(x) ≤ δ 0 (x) for all x ∈ X. This result is then applied to obtain bounds on an optimal policy in the class of dynamic programs which are bounded, monotone contractions.