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...

We present an algorithm for a pair of pursuers, each with one flashlight, searching for an unpredictable, moving target in a 2D environment (simple polygon). Given a polygon with n edges and m concave regions, the algorithm decides in time O(n + nm + m) whether the polygon can be cleared by the two 1-searchers, and if so, constructs a search schedule. The pursuers are allowed to move on the bou...

We consider the impact of job rotation in a directed search model in which …rm sizes are endogenously determined and match quality is initially unknown. A large …rm bene…ts from the opportunity of rotating workers so as to partially overcome loss of mismatch. As a result, in the unique symmetric equilibrium, large …rms have higher labor productivity and lower separation rates. In contrast to th...

In this article we establish the existence of at least two distinct solutions to singular elliptic equations involving a concave term and critical Caffarelli-Kohn-Nirenberg exponent with sign-changing weight functions.

Team Coverage Games (TCGs) are a representation of cooperative games, where the value a coalition generates depends on both individual contributions of its members and synergies between them. The synergies are expressed in terms of the importance of the agents in various teams. TCGs model the synergy as a reduction in utility that occurs when team members are missing, causing the team not to ac...

A triangle {a(n, k)}0≤k≤n of nonnegative numbers is LC-positive if for each r, the sequence of polynomials ∑n k=r a(n, k)q k is q-log-concave. It is double LC-positive if both triangles {a(n, k)} and {a(n, n − k)} are LC-positive. We show that if {a(n, k)} is LC-positive then the log-concavity of the sequence {xk} implies that of the sequence {zn} defined by zn = ∑n k=0 a(n, k)xk, and if {a(n, ...

The general coalition-game model suggested in [2] is considered, and a few types of combinations and transformations of such games are investigated. It is shown that a conjunction, disjunction, and combination of two general coalition-games is, under natural conditions, also a general coalition-game. Also the main relations between the solutions of the original games and the resulting one are d...

In this paper, we establish the following perturbation result concerning the singular values of a matrix: Let A,B ∈ R be given matrices, and let f : R+ → R+ be a concave function satisfying f(0) = 0. Then, we have min{m,n}

In this paper we have proposed a clustreing technique that extracts suband sup-clusters based on a simple measure of circular symmetry. These sub-clusters and sup-clusters are then used as building blocks to form final clusters of any arbitry shape including concave ones through merging and splitting iteratively. The proposed method is tested on multi-spectral satellite imagery and a good resul...

We study an implementation problem for settings where some of the participants have non concave valuations. These valuations are common in the wireless industry in cases where primary users with property rights on a spectrum band would like to lease some of it to low power users. The non concavity void the efficiency results for standard designs of dynamic auctions. Moreover, policy concerns in...