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optimization in discrete time
**Takashi** **Kamihigashi**
Given a sequence {fn}n∈N of measurable functions on a σ -finite measure space such that the integral of each fn as well as that of lim supn↑∞ fn exists in R

The discrete time “bomber problem” has been one of the longest standing open problems in operations research. In particular, the validity of one of the natural monotonicity conjectures—known as property (B)—has been an unresolved issue since 1968. In this paper we report 41 counterexamples to property (B) of this problem. We have found them by computing the exact solutions for...

In this note, we discuss an order-theoretic approach to dynamic programming. In particular, we explain how order-theoretic fixed point theorems can be used to establish the existence of a fixed point of the Bellman operator, as well as why they are not sufficient to characterize the value function. By doing this, we present the logic behind the simple yet useful result recently...

Consider a preordered metric space ( X , d , ⪯ ) . Suppose that d ( x , y ) ≤ d ( x ′ , y ′ ) if x ′ ⪯ x ⪯ y ⪯ y ′ . We say that a self-map T on X is asymptotically contractive if d ( T i x , T i y ) → 0 as i ↑ ∞ for all x , y ∈ X . We show that an order-preserving self-map T on X has a globally stable fixed point if and only if T is asymptotically contractive and there exist x...