A polynomial is unimodal if its sequence of coefficients are increasing up to an index, and then are decreasing after that index. A polynomial is logconcave if the sequence of the logarithms of the coefficients is concave. We prove that if P (x) is a polynomial with nonnegative non-decreasing coefficients then P (x+z) is unimodal for any natural z. Furthermore, we prove that if P (x) is a log-c...

The stable allocation model is a many-to-many matching model in which each pair’s partnership is represented by a nonnegative integer. This paper establishes a link between two different formulations of this model; the choice function model studied thoroughly by Alkan and Gale and the discrete-concave (M♮-concave) value function model introduced by Eguchi, Fujishige and Tamura. We show that the...

We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly st...

We examine the Concave Topology Capacity and Flow Assignment (TCFA) problem. Only two algorithms in the literature are appropriate for solving TCFA problems with concave link cost functions: Kleinrock and Gerla’s Concave Branch Elimination (CBE) procedure, [26][20], and a greedy link elimination procedure developed by Gersht [21]. However, neither works well in practice. The CBE procedure does ...

Convex and concave hulls are useful concepts for a wide variety of application areas, such as pattern recognition, image processing, statistics, and classification tasks. Concave hull performs better than convex hull, but it is difficult to formulate and few algorithms are suggested. Especially, an n-dimensional concave hull is more difficult than a 2or 3dimensional one. In this paper, we propo...

The preference of a concave nontransitive consumer is represented by a skew-symmetric and concave-convex bifunction on the set of all commodity bundles. This paper characterizes finite sets of demand observations that are consistent with the demand behavior of such kind of consumer by a generalized monotonicity property.

Segmentation of overlapping convex objects has gained a lot of attention in numerous biomedical and industrial applications. A partial overlap between two or more convex shape objects leads to a shape with concave edge points that correspond to the intersections of the object boundaries. Therefore, it is a common practice to utilize these concave points to segment the contours of overlapping ob...

An approach to the Shannon and Rényi entropy maximization problems with constraints on the mean and law invariant deviation measure for a random variable has been developed. The approach is based on the representation of law invariant deviation measures through corresponding convex compact sets of nonnegative concave functions. A solution to the problem has been shown to have an alpha-concave d...

High speed and absence of a precise control over pressure distribution confine sheet Electromagnetic Forming into a die to simple shapes having shallow depth. It is possible to reach a higher depth by using a convex punch instead of a concave die. In this study, sheet Electromagnetic Forming on a punch and sheet Electromagnetic Forming into a die are investigated. The electromagnetic part of th...

We consider resource allocation with separable objective functions defined over subranges of the integers. While it is well known that (the maximization version of) this problem can be solved efficiently if the objective functions are concave, the general problem of resource allocation with non-concave functions is difficult. In this article we show that for fairly well-shaped non-concave objec...