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Fast computation of the leastcore and prenucleolus of cooperative games

Joseph Frédéric Bonnans, Matthieu André (2008)

RAIRO - Operations Research

The computation of leastcore and prenucleolus is an efficient way of allocating a common resource among n players. It has, however, the drawback being a linear programming problem with 2n - 2 constraints. In this paper we show how, in the case of convex production games, generate constraints by solving small size linear programming problems, with both continuous and integer variables. The approach is extended to games with symmetries (identical players), and to games with partially continuous...

Finding target units in FDH model by least-distance measure model

Ali Ebrahimnejad, Reza Shahverdi, Farzad Rezaee Balf, Maryam Hatefi (2013)

Kybernetika

Recently, some authors used the Least-Distance Measure model in order to obtain the shortest distance between the evaluated Decision Making Unit (DMU) and the strongly efficient production frontier. But, their model is not applicable for situation in which the production possibility set satisfies free disposability property. In this paper, we propose a new approach to this end in FDH model which improves the application potential of the Least-Distance Measure and overcomes the mentioned shortcoming....

Fourier analysis, linear programming, and densities of distance avoiding sets in ℝ n

Fernando Mário de Oliveira Filho, Frank Vallentin (2010)

Journal of the European Mathematical Society

We derive new upper bounds for the densities of measurable sets in ℝ n which avoid a finite set of prescribed distances. The new bounds come from the solution of a linear programming problem. We apply this method to obtain new upper bounds for measurable sets which avoid the unit distance in dimensions 2 , ⋯ , 24 . This gives new lower bounds for the measurable chromatic number in dimensions 3 , ⋯ , 24 . We apply it to get a short proof of a variant of a recent result of Bukh which in turn generalizes theorems of Furstenberg,...

Full-Newton step infeasible interior-point algorithm for SDO problems

Hossein Mansouri (2012)

Kybernetika

In this paper we propose a primal-dual path-following interior-point algorithm for semidefinite optimization. The algorithm constructs strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Each main step of the algorithm consists of a feasibility step and several centering steps. At each iteration, we use only full-Newton step. Moreover, we use a more natural feasibility step, which targets at the μ + -center. The iteration bound of the algorithm coincides...

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