We provide a new approach to the analysis of the optimal joint inventory and transshipment control with uncertain capacities by employing the concept of L-convexity. In this approach, we use variable transformation techniques and apply two recent results to establish the L-concavity of the profit-to-go functions, which significantly simplifies the analysis in the existing literature. Some varia...

In this work, we study continuous reformulations of zero-one concave programming problems. We introduce new concave penalty functions and we prove, using general equivalence results here derived, that the obtained continuous problems are equivalent to the original combinatorial problem.

We reassess the respective gains from R&D cooperation and competition in a Cournot Duopoly with homogeneous goods, where firms adopt a concave cost-reducing R&D technology. Contrary to the previous literature on the same topic, our main results are that (i) no corner solutions emerge and (ii) cooperation, in the form of either a cartel or a joint venture, is always profitable for firms and (iii...

and Applied Analysis 3 given the linear character ofy(a)+(y(b)−y(a))((s−a)/(b− a󸀠)) and the fact that y(x), y󸀠(x) ≥ 0 on [a, b]. Equation (14) gives (7). Let us focus now on (8). Again, for the sake of simplicity we will only consider the case y(x) ≥ 0 on [a, b]. From the concavity of y(x) (Lemma 1) one has y (s) ≥ y (b 󸀠 ) + y (a󸀠) − y (b󸀠) b − a (b 󸀠 − s) , s ∈ [a 󸀠 , b 󸀠 ] , (15) that is, Φ(...

Dijkstra’s algorithm is a well-known algorithm for the single-source shortest path problem in a directed graph with nonnegative edge length. We discuss Dijkstra’s algorithm from the viewpoint of discrete convex analysis, where the concept of discrete convexity called L-convexity plays a central role. We observe first that the dual of the linear programming (LP) formulation of the shortest path ...

Simion [9] conjectured the unimodality of a sequence counting lattice paths in a grid with a Ferrers diagram removed from the northwest corner. Recently, Hildebrand [5] and then Wang [11] proved the stronger result that this sequence is actually log concave. Both proofs were mainly algebraic in nature. We give two combinatorial proofs of this theorem.

We provide a combinatorial proof for the fact that for any fixed n, the sequence {i(n, k)}0≤k≤(n2) of the numbers of permutations of length n having k inversions is log-concave.

The main purpose of this paper is to prove the existence of the fuzzy core of an exchange economy with a heterogeneous divisible commodity in which preferences of players are concave measures defined on a σ-algebra of admissible pieces of the total endowment of the commodity. The problem is formulated as the partitioning of a measurable space among finitely many players. Applying the Yosida– He...

In this paper we establish concavity properties of two extensions of the classical notion of the outer parallel volume. On the one hand, we replace the Lebesgue measure by more general measures. On the other hand, we consider a functional version of the outer parallel sets.

Bounds are found for the distribution function of the sum of squares X2+y2 where X and Y are arbitrary continuous random variables. The techniques employed, which utilize copulas and their properties, show that the bounds are pointwise best-possible when X and Y are symmetric about 0 and yield expressions which can be evaluated explicitly when X and Y have a common distribution function which i...