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Displaying 141 –
160 of
303
Les méthodes de points intérieurs en programmation linéaire
connaissent un grand succès depuis l'introduction
de l'algorithme de Karmarkar. La convergence de l'algorithme repose sur une
fonction potentielle qui, sous sa
forme multiplicative, fait apparaître un exposant p. Cet exposant
est, de façon
générale, choisi supérieur au nombre de variables n du problème.
Nous montrons dans cet
article que l'on peut utiliser des valeurs de
p plus petites que n. Ceci permet d'améliorer le conditionnement...
In this paper, the robust counterpart of the linear fractional programming problem under linear inequality constraints with the interval and ellipsoidal uncertainty sets is studied. It is shown that the robust counterpart under interval uncertainty is equivalent to a larger linear fractional program, however under ellipsoidal uncertainty it is equivalent to a linear fractional program with both linear and second order cone constraints. In addition, for each case we have studied the dual problems...
The standard multiple criteria optimization starts with an
assumption that the criteria are incomparable. However, there are many
applications in which the criteria express ideas of allocation of
resources meant to achieve some equitable distribution. This paper
focuses on solving linear multiple criteria optimization problems with
uniform criteria treated in an equitable way. An axiomatic definition of
equitable efficiency is introduced as an refinement of
Pareto-optimality. Various generation...
In this paper we investigate a class of problems permitting a good characterisation from the point of view of morphisms of oriented matroids. We prove several morphism-duality theorems for oriented matroids. These generalize LP-duality (in form of Farkas' Lemma) and Minty's Painting Lemma. Moreover, we characterize all morphism duality theorems, thus proving the essential unicity of Farkas' Lemma. This research helped to isolate perhaps the most natural definition of strong maps for oriented matroids....
We discuss some implications of linear programming for Mather theory [13, 14, 15] and its finite dimensional approximations. We find that the complementary slackness condition of duality theory formally implies that the Mather set lies in an -dimensional graph and as well predicts the relevant nonlinear PDE for the “weak KAM” theory of Fathi [6, 7, 8, 5].
We discuss some implications of linear programming for Mather theory
[13-15] and its
finite dimensional approximations. We find that the complementary
slackness condition of duality theory formally implies that the Mather set lies in an
n-dimensional graph and as well predicts the relevant nonlinear PDE for the “weak
KAM” theory of Fathi [5-8].
A continuum mechanical model based on the Helfrich Hamiltonian is devised to investigate the coupling between lipid composition and membrane curvature. Each monolayer in the bilayer is modeled as a freely deformable surface with a director field for lipid orientation. A scalar field for the mole fraction of two lipid types accounts for local changes in composition. It allows lipids to access monolayer regions favorable to their intrinsic curvature at the expense of increasing entropic free energy....
The least-squares method is used to obtain a stable algorithm for a system of linear inequalities as well as linear and nonlinear programming. For these problems the solution with minimal norm for a system of linear inequalities is found by solving the non-negative least-squares (NNLS) problem. Approximate and exact solutions of these problems are discussed. Attention is mainly paid to finding the initial solution to an LP problem. For this purpose an NNLS problem is formulated, enabling finding...
Currently displaying 141 –
160 of
303