We consider point sets in (Z^2,n) where no three points are on a line – also called caps or arcs. For the determination of caps with maximum cardinality and complete caps with minimum cardinality we provide integer linear programming formulations and identify some values for small n.
A cooperative game is defined as a set of players and a cost function. The distribution of the whole cost between the players can be done using the core concept, that is the set of all undominated cost allocations which prevent players from grouping. In this paper we study a game whose cost function comes from the optimal solution of a linear integer covering problem. We give necessary and sufficient conditions for the core to be nonempty and characterize its allocations using linear programming...
We present an exact method for integer linear programming problems that combines branch and bound with column generation at each node of the search tree. For the case of models involving binary column vectors only, we propose the use of so-called geometrical cuts to be added to the subproblem in order to eliminate previously generated columns. This scheme could be applied to general integer problems without specific structure. We report computational results on a successful application of this approach...
We present an exact method for integer linear programming problems that combines branch and bound with column generation at each node of the search tree. For the case of models involving binary column vectors only, we propose the use of so-called geometrical cuts to be added to the subproblem in order to eliminate previously generated columns. This scheme could be applied to general integer problems without specific structure. We report computational results on a successful application of this...
We give a review of results proved and published mostly in recent years, concerning real-valued convex functions as well as almost convex functions defined on a (not necessarily convex) subset of a group. Analogues of such classical results as the theorems of Jensen, Bernstein-Doetsch, Blumberg-Sierpiński, Ostrowski, and Mehdi are presented. A version of the Hahn-Banach theorem with a convex control function is proved, too. We also study some questions specific for the group setting, for instance...
El QAP-Arbol es un caso especial del problema de asignación cuadrática en que los flujos distintos de cero forman un árbol. No se requiere ninguna condición para la matriz de distancias. En este artículo presentamos una formulación del QAP-Arbol como un problema de programación lineal entera. Basándonos en esta formulación hemos construido cuatro relajaciones lagrangianas distintas que nos permiten obtener una serie de cotas inferiores para este problema. Para resolver una de estas relajaciones,...