In this paper we study the existence of subharmonic solutions of the Hamiltonian system $$ J\dot x+ u^* \nabla G(t,u(x)) =e(t)$$ where u is a linear map, G is a C 1-function and e is a continuous function.

Dans cet article, nous proposons une nouvelle méthode de purification pour les problèmes de complémentarité linéaire, monotones. Cette méthode associe à chaque itéré de la suite, générée par une méthode de points intérieurs, une base non nécessairement réalisable. Nous montrons que, sous les hypothèses de complémentarité stricte et de non dégénérescence, la suite des bases converge en un nombre fini d'itérations vers une base optimale qui donne une solution exacte du problème. Le procédé adopté sert également à préconditionner l'algorithme de gradient conjugué lors du calcul de la direction de Newton.

We propose a variational model for one of the most importantproblems in traffic networks, namely, the network equilibrium flow that is, traditionallyin the context of operations research, characterized by minimum cost flow. This model has the peculiarity of being formulated by means of a suitable variational inequality (VI) andits solution is called “equilibrium”. This model becomes a minimum cost model when the cost function is separableor, more general, when the Jacobian of the cost operator is symmetric;in such cases a functional representing the total network utility exists.In fact in these cases we can write the first order optimality conditions which turn out to be a VI.In the other situations (i.e., when global utility functional does not exist),which occur much more often in the real problems, we can study the network by looking for equilibrium solutions instead of minimum points.The Lagrangean approach to the study of the VI allows us to introduce dual variables, associated to the constraints of the feasible set, which may receive interesting interpretations in terms of potentials associated to the arcs and the nodes of the network.This interpretation is an extension and generalization of the classic Bellman conditions. Finally, we deepen the analysis of the networks having capacity constraints.


Pour établir des plans de production et d'approvisionnements, une entreprise utilise un système de prévisions. Celui-ci est constitué d'une méthode de prévision de la demande et d'une méthode de lot-sizing permettant l'obtention de plans prévisionnels. Nous proposons une démarche permettant d'évaluer la fiabilité des prévisions fournies par un tel système. Cette analyse se base sur l'étude de l'impact des aléas de la demande sur les coûts induits par les plans prévisionnels. Nous avons appliqué ce protocole à un système de prévisions constitué du lissage exponentiel et de la méthode de Florian et Klein [5]. Dans les conditions expérimentales considérées, ce système de prévision fournit des informations fiables.

Cet article est un travail de synthèse autour de l'analyse desensibilité pour les problèmes linéaires envariables 0-1. De nombreux aspects sont ainsi abordés : historiqueet formes d'analyse de sensibilité, exemples d'application,complexité, conditions d'optimalité, algorithmes etapproches. Nous dressons par ailleurs quelques perspectives derecherche actuelles dans ce domaine.

We present briefly some results we obtained with known methods to solve minimum cost tension problems, comparing their performance on non-specific graphs and on series-parallel graphs. These graphs are shown to be of interest to approximate many tension problems, like synchronization in hypermedia documents. We propose a new aggregation method to solve the minimum convex piecewise linear cost tension problem on series-parallel graphs in O(m3) operations.

Nous construisons des familles de facettes du polytope du sac-à-dos quadratique en 0-1 selon les deux approches suivantes.Le Boolean quadric polytope (introduit dans le cas sans contraintes par Padberg [12]) contenant le polytope du sac-à-dos quadratique, une première approche consiste à se demander sous quelles conditions une facette du premier est aussi une facette du second et quand ces conditions ne sont pas remplies quels liftings permettent d'en faire une facette. Des réponses à ces questions sont données dans le cas de l'inégalité "coupe" introduite par Padberg.Dans une seconde approche, suivant la méthode de linéarisation d'Adams et Sherali [1], nous multiplions par une variable directe ou complémentée une facette du polytope du sac-à-dos linéaire. Nous montrons que cette approche permet d'obtenir des facettes du polytope du sac-à-dos quadratique et nous l'étendons par la suite à la multiplication de facettes du sac-à-dos quadratique lui-même.Des résultats numériques illustrent la mise en oeuvre dans un algorithme de coupes, d'inégalités ainsi obtenues.

We present a hybrid approach for the FrequencyAssignment Problem with Polarization. This problem, viewed asMax-CSP, is treated as a sequence of decision problems, CSPlike. The proposed approach combines the Arc-Consistencytechniques with a performed Tabu Search heuristic. The resultingalgorithm gives some high quality solutions and has proved itsrobustness on instances with approximately a thousand variablesand nearly ten thousand constraints.

Dans cet article nous caractérisons, par les facettes, l'enveloppe convexe des vecteurs caractéristiques des hyperplans d'un espace projectif fini et d'un espace affine fini.

Le traditionnel problème d'ordonnancement de type flowshop se généralise en un problème d'optimisation matricielle dansl'algèbre Max-Plus. Une famille de bornes inférieures est présentée pour ce nouveau problème et la preuve est apportée que ces bornes généralisent les bornes de Lageweg et al.

In this paper, a graph partitioning problem that arises in the design ofSONET/SDH networks is defined and formalized. Approximation algorithms withperformance guarantees are presented. To solve this problem efficiently inpractice, fast greedy algorithms and a tabu-search method are proposed andanalyzed by means of an experimental study.

In this paper we consider the problem of scheduling precedence task graphs inparallel processing where there can be disturbances in computation andcommunication times. Such a phenomenon often occurs in practice, due to ourinability to exactly predict the time because of system intrusion like cache miss and packet transmission time in mediums like ethernet etc. We propose a method based on the addition of some extra edges to protect the initial scheduling from performing badly due to such changes and provide an upper bound on theperformance guarantee for the scheduling algorithms. Moreover, this construction guarantees a result at least as goodas the result obtained for the initial static scheduling.We also show that this construction is a minimal set in context of partially on-line scheduling.

This paper studies the issue of well-posednessfor vector optimization. It is shown thatcoercivity implies well-posedness without any convexity assumptionson problem data.For convex vector optimization problems,solution sets of such problems are non-convex in general,but they are highly structured. By exploring such structures carefully via convex analysis,we are able to obtaina number of positive results, including a criterion for well-posedness in terms of that of associated scalar problems.In particularwe show that a well-known relative interiority conditioncan be used as a sufficient condition for well-posedness in convexvector optimization.

In this paper we consider a like-queue production system in which server startupand breakdowns are possible. The server is turned on (i.e. begins startup)when N units are accumulated in the system and off when the system is empty.We model this system by an M[x]/M/1 queue withserver breakdowns and startup time under the N policy. The arrival rate varies according to the server's status:off, startup, busy, or breakdown.While the server is working, he is subject tobreakdowns according to a Poisson process. When the server breaks down, he requires repairat a repair facility, where the repair time follows the negative exponential distribution.We study the steady-state behaviour of the system size distribution atstationary point of time as well as the queue size distribution at departure point of timeand obtain some useful results.The total expected cost function per unit time is developed to determine the optimal operatingpolicy at a minimum cost. This paper provides the minimum expected cost and the optimal operatingpolicy based on assumed numerical values of the system parameters. Sensitivity analysis is also provided.

In this paper, we study the problem of computing a minimum cost Steiner tree subject to a weight constraint in a Halin graph where each edge has a nonnegative integer cost and a nonnegative integer weight. We prove the NP-hardness of this problem and present a fully polynomial time approximation scheme for this NP-hard problem.

We present a transformation for stochastic matrices and analyze theeffects of using it in stochastic comparison with the strong stochastic(st) order. We show that unless the given stochastic matrix is row diagonallydominant, the transformed matrix provides better st bounds on the steady state probability distribution.

Les méthodes de points intérieurs en programmation linéaireconnaissent un grand succès depuis l'introductionde l'algorithme de Karmarkar. La convergence de l'algorithme repose sur unefonction potentielle qui, sous saforme multiplicative, fait apparaître un exposant p. Cet exposantest, de façongénérale, choisi supérieur au nombre de variables n du problème.Nous montrons dans cetarticle que l'on peut utiliser des valeurs dep plus petites que n. Ceci permet d'améliorer le conditionnement dela méthode au voisinage de la solution optimale.

In this paper, we study a heuristic algorithm for global optimization, which is based on the Ψ-transformation. We illustrate its behavior first, on a set of continuous non-convex objective functions – we search the global optimum of each function. Then, we give an example from combinatorial optimization. It concerns the optimization of scheduling rules parameters of a manufacturing system. Computational results are presented, they look encouraging.

A recently introduced dualization technique for binary linear programs with equality constraints, essentially due to Poljak et al. [13], and further developed in Lemaréchal and Oustry [9], leads to simple alternative derivations of well-known, important relaxations to two well-known problems of discrete optimization: the maximum stable set problem and the maximum vertex cover problem. The resulting relaxation is easily transformed to the well-known Lovász θ number.

This paper is concerned with scheduling when the data are not fully knownbefore the execution. In that case computing a complete schedule off-linewith estimated data may lead to poor performances. Some flexibility must beadded to the scheduling process. We propose to start from a partial schedule and to postpone the complete scheduling until execution, thus introducing what we call a stabilizationscheme. This is applied to the m machine problem with communicationdelays: in our model an estimation of the delay is known at compile time; but disturbances due to network contention, link failures, ... may occur at execution time. Hence the processor assignment and a partial sequencing on each processor are determined off-line. Some theoreticalresults for tree-like precedence constraints and an experimental study show the interest of this approach compared with fully on-line scheduling.