Abstract. A function is exponentially concave if its exponential is concave. We consider exponentially concave functions on the unit simplex. It is known that gradient maps of exponentially concave functions are solutions of a MongeKantorovich optimal transport problem and allow for a better gradient approximation than those of ordinary concave functions. The approximation error, called L-diver...

Recently K. Murota has introduced concepts of L-convex function and Mconvex function as generalizations of those of submodular function and base polyhedron, respectively, and has shown separation theorems for L-convex/concave functions and for M-convex/concave functions. The present note gives short alternative proofs of the separation theorems by relating them to the ordinary separation theore...

Let L be a divergence form elliptic operator with complex bounded measurable coefficients, ω the positive concave function on (0,∞) of strictly critical lower type pω ∈ (0, 1] and ρ(t) = t /ω(t) for t ∈ (0,∞). In this paper, the authors introduce the generalized VMO spaces VMOρ,L(R) associated with L, and characterize them via tent spaces. As applications, the authors show that (VMOρ,L(R)) = Bω...

The concepts of L-convex function and M-convex function have recently been introduced by Murota as generalizations of submodular function and base polyhedron, respectively, and discrete separation theorems are established for L-convex/concave functions and for M-convex/concave functions as generalizations of Frank's discrete separation theorem for submodular/supermodular set functions and Edmon...

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 ...

This paper deals with the single-item capacitated lot sizing problem with concave production and storage costs, considering minimum order quantity and dynamic time windows. This problem models a lot sizing where the production lots are constrained in amount and frequency. In this problem, a demand must be satisfied at each period t over a planning horizon of T periods. This demand can be satisf...

We present a logspace algorithm that constructs a canonical intersection model for a given proper circular-arc graph, where canonical means that models of isomorphic graphs are equal. This implies that the recognition and the isomorphism problems for this class of graphs are solvable in logspace. For a broader class of concave-round graphs, that still possess (not necessary proper) circular-arc...

In this paper, we develop two algorithms for globally optimizing a special class of linear programs with an additional concave constraint. We assume that the concave constraint is defined by a separable concave function. Exploiting this special structure, we apply Falk-Soland’s branch-and-bound algorithm for concave minimization in both direct and indirect manners. In the direct application, we...

Given a sequence (ak) = a0, a1, a2, . . . of real numbers, define a new sequence L(ak) = (bk) where bk = ak − ak−1ak+1. So (ak) is log-concave if and only if (bk) is a nonnegative sequence. Call (ak) infinitely log-concave if L(ak) is nonnegative for all i ≥ 1. Boros and Moll [3] conjectured that the rows of Pascal’s triangle are infinitely log-concave. Using a computer and a stronger version o...