A family of subadditive functions which contains the optimal solution of subadditive duals for integer programs has been presented by Klabjan (2007). In this paper we present a subadditive dual ascent procedure to find an optimal subadditive dual function based on Klabjan’s generator subadditive function. Then we use the proposed method to solve the so called uncapacitated facility location pro...

Let X be a Banach space, (I, μ) be a finite measure space, and Φ be an increasing subadditive continuous function on [0,+∞) with Φ(0) = 0. In the present paper, we discuss the best p-simultaneous approximation of L(I,G) in L(I,X) where G is a closed subspace of X .

Let ν be a finite, finitely subadditive outer measure on P(X). Define ρ(E)= ν(X)− ν(E′) for E ⊂ X. The measurable sets Sν and Sρ and the set S = {E ⊂ X/ν(E) = ρ(E)} are investigated in general, and in the presence of regularity or modularity assumptions on ν . This is also done for ν0(E) = inf{ν(M)/E ⊂ M ∈ Sν}. General properties of ν are derived when ν is weakly submodular. Applications and nu...

We study the power and limitations of posted prices in multi-unit markets, where agents arrive sequentially in an arbitrary order. We prove upper and lower bounds on the largest fraction of the optimal social welfare that can be guaranteed with posted prices, under a range of assumptions about the designer’s information and agents’ valuations. Our results provide insights about the relative pow...

Let φ be an arbitrary bijection of R+. We prove that if the two-place function φ−1[φ(s) + φ(t)] is subadditive in R+ then φ must be a convex homeomorphism of R+. This is a partial converse of Mulholland’s inequality. Some new properties of subadditive bijections of R+ are also given. We apply the above results to obtain several converses of Minkowski’s inequality. Introduction. Throughout this ...

We introduce a novel framework of Prophet Inequalities for combinatorial valuation functions. For a (non-monotone) submodular objective function over an arbitrary matroid feasibility constraint, we give an O(1)-competitive algorithm. For a monotone subadditive objective function over an arbitrary downward-closed feasibility constraint, we give an O(log n log r)-competitive algorithm (where r is...

Subadditive time discounting means that discounting over a delay is greater when the delay is divided into subintervals than when it is left undivided. This may produce the most important result usually attributed to hyperbolic discounting: declining impatience, or the inverse relationship between the discount rate and the magnitude of the delay. Three choice experiments were conducted to test ...