Families of vortex equilibria, with constant vorticity, in steady flow past a flat plate are computed numerically. An equilibrium configuration, which can be thought of as a desingularized point vortex, involves a single symmetric vortex patch located wholly on one side of the plate. Given that the outermost edge of the vortex is unit distance from the plate, the equilibria depend on three parameters: the length of the plate, circulation about the plate, and the distance of the innermost edge of the vortex from the plate. Families in which there is zero circulation about the plate and for which the Kutta condition at the plate ends is satisfied are both considered. Properties such as vortex area, lift and free-stream speed are computed. Time-dependent numerical simulations are used to investigate the stability of the computed steady solutions.

In this paper, by using the Leggett–Williams fixed point theorem, we prove the existence of three nonnegative solutions to second-order nonlinear impulsive differential equations with a three-point boundary value problem.

A sharp L2 inequality of Ostrowski type is established, which provides a generalization of some previous results and gives some other interesting results as special cases. Applications in numerical integration are also given.

This paper presents a migration strategy for a set of mobile agents (MAs) in order to satisfy customers' requests in a transport network, through a multimodal information system. In this context, we propose an optimization solution which operates on two levels. The first one aims to constitute a set of MAs building their routes, called Workplans. At this level, Workplans must incorporate all nodes, representing information providers in the multimodal network, in order to explore it completely. Thanks to an evolutionary approach, the second level must optimize nodes selection in order to increase the number of satisfied users. The assignment of network nodes to the required services must be followed by a Workplan update procedure in order to deduce final routes paths. Finally, simulation results are mentioned to invoke the different steps of our adopted approach.

We present in this paper a new multiobjective memetic algorithm scheme called MEMOX. In current multiobjective memetic algorithms, the parents used for recombination are randomly selected. We improve this approach by using a dynamic hypergrid which allows to select a parent located in a region of minimal density. The second parent selected is a solution close, in the objective space, to the first parent. A local search is then applied to the offspring. We experiment this scheme with a new multiobjective tabu search called PRTS, which leads to the memetic algorithm MEMOTS. We show on the multidimensional multiobjective knapsack problem that if the number of objectives increase, it is preferable to have a diversified research rather using an advanced local search. We compare the memetic algorithm MEMOTS to other multiobjective memetic algorithms by using different quality indicators and show that the performances of the method are very interesting.

In this paper, a new approach to a characterization of solvability of a nonlinear nonsmooth multiobjective programming problem with inequality constraints is introduced. A family of η-approximated vector optimization problems is constructed by a modification of the objective and the constraint functions in the original nonsmooth multiobjective programming problem. The connection between (weak) efficient points in the original nonsmooth multiobjective programming problem and its equivalent η-approximated vector optimization problems is established under V-invexity. It turns out that, in most cases, solvability of a nonlinear nonsmooth multiobjective programming problem can be characterized by solvability of differentiable vector optimization problems.

By means of a symbolic calculus for finding solutions of difference equations, we derive explicit eigenvalues, eigenvectors and inverses for tridiagonal Toeplitz matrices with four perturbed corners.

We present here a pricing model which is an extension of the cooperative game concept and which includes a notion of elastic demand. We present some existence results as well as an algorithm, and we conclude by discussing a specific problem related to network pricing.

We present an inexact interior point proximal method to solve linearly constrained convex problems. In fact, we derive a primal-dual algorithm to solve the KKT conditions of the optimization problem using a modified version of the rescaled proximal method. We also present a pure primal method. The proposed proximal method has as distinctive feature the possibility of allowing inexact inner steps even for Linear Programming. This is achieved by using an error criterion that bounds the subgradient of the regularized function, instead of using ϵ-subgradients of the original objective function. Quadratic convergence for LP is also proved using a more stringent error criterion.

The recourse to operation research solutions has strongly increasedthe performances of scheduling task in the High-Level Synthesis(called hardware compilation). Scheduling a whole program is notpossible as too many constraints and objectives interact. We decomposehigh-level scheduling in three steps. Step 1: Coarse-grain schedulingtries to exploit parallelism and locality of the whole program (inparticular in loops, possibly imperfectly nested) with a rough view ofthe target architecture. This produces a sequence of logical steps,each of which contains a pool of macro-tasks. Step 2: Micro-schedulingmaps and schedules each macro-task independently taking into accountall peculiarities of the target architecture. This produces areservation table for each macro-task. Step 3: Fine-grain schedulingrefines each logical step by scheduling all its macro-tasks. Thispaper focuses on the third step.As tasks are modeled as reservation tables, we can express resourceconstraints using dis-equations (i.e., negations of equations). Asmost scheduling problems, scheduling tasks with reservation tables tominimize the total duration is NP-complete. Our goal here is todesign different strategies and to evaluate them, on practicalexamples, to see if it is possible to find optimal solution inreasonable time. The first algorithm is based on integer linearprogramming techniques for scheduling, which we adapt to our specificproblem. Our main algorithmic contribution is an exactbranch-and-bound algorithm, where each evaluation is accelerated byvariant of Dijkstra's algorithm. A simple greedy heuristic is alsoproposed for comparisons. The evaluation and comparison are done onpieces of scientific applications from the PerfectClub and theHLSynth95 benchmarks. The results demonstrate the suitability of thesesolutions for high-level synthesis scheduling.

Minimizing shutterings assembling time on construction sites can yield significant savings in labor costs and crane moves. It requires solving a pairing problem that optimizes the ability for the crane to move chains of shutterings as a whole when they can be later reused together to frame another wall of the site. In this paper, we show that this problem is NP-hard in the strong sense as well as both its multiflow and ordering aspects. We also introduce a linear relaxation that computes reasonably good lower bounds of the objective, and describe a Tabu Search based on pairings insertion and ejection that builds promising solutions.

It is well known that each tree metric M has a unique realization as a tree, and that this realization minimizes the total length of the edges among all other realizations of M. We extend this result to the class of symmetric matrices M with zero diagonal, positive entries, and such that mij + mkl ≤ max{mik + mjl, mil + mjk} for all distinct i,j,k,l.

In telecommunications network design, one of the most frequentproblems is to adjust the capacity on the links of the network in order to satisfy a set of requirements. In the past, theserequirements were demands based on historical data and/or demographic predictions. Nowadays, because of new technologydevelopment and customer movement due to competitiveness, thedemands present considerable variability. Thus, network robustness w.r.t demand uncertainty is now regarded as a majorconsideration. In this work, we propose a min-max-min formulation and a methodology to cope with this uncertainty. We model the uncertainty as the convex hull of certain scenarios and show thatcutting plane methods can be applied to solve the underlying problems. We will compare Kelley, Elzinga-Moore and bundle methods.


The Progressive Second Price mechanism (PSP), recently introduced byLazar and Semret to share aninfinitely-divisible resource among users through pricing, has been shown to verifyvery interesting properties. Indeed, the incentive compatibilityproperty of that scheme, and the convergence toan efficient resource allocation where established, using the frameworkof Game Theory.Therefore, that auction-based allocation and pricing scheme seemsparticularly well-suited to solve congestion problems intelecommunication networks, where the resource to share is theavailable bandwidth on a link.This paper aims atsupplementing the existing results by highlighting some properties of thedifferent equilibria that can be reached. We precisely characterize the possible outcomes of thePSP auction game in terms of players bid price: when the bid fee (cost of a bid update) tends to zero then the bid price of all users at equilibrium gets close to the so-called market clearing price of the resource. Therefore, observing an equilibrium of the PSP auction game gives some accurate information about the market clearing price of the resource.

In this paper we, firstly, present a recursive formula of theempirical estimator of the semi-Markov kernel. Then a non-parametricestimator of the expected cumulative operational time forsemi-Markov systems is proposed. The asymptotic properties of thisestimator, as the uniform strongly consistency and normality aregiven. As an illustration example, we give a numerical application.

Most systems are characterized by uncertainties that cause throughput to be highly variable, for example, many modern production processes and services are substantially affected by random yields. When yield is random, not only is the usable quantity uncertain, but the random yield reduces usable capacity and throughput in the system. For these reasons, strategies are needed that incorporate random yield. This paper presents the analysis of the newsvendor model with a general random yield distribution, including the derivation of the optimal order quantity. Results are shown to converge to the basic newsvendor model for the case of perfect yield, and are further demonstrated using the case of general multiplicative random yield. Results have significant impact on both manufacturing and service sectors since the newsvendor model applies to many real-world situations.

The m-subspace polytope is defined as the convex hull of the characteristic vectors of all m-dimensional subspaces ofa finite affine space. The particular case of the hyperplane polytopehas been investigated by Maurras (1993) and Anglada and Maurras (2003), who gave a complete characterization of the facets. The general m-subspace polytope that we consider shows a much more involved structure, notably as regards facets. Nevertheless, several families of facets are established here. Then the group of automorphisms of the m-subspace polytope is completely described and the adjacency of vertices is fully characterized.


Clique family inequalities a∑v∈W xv + (a - 1)∈v∈W , xv ≤ aδ form an intriguing class of valid inequalities for the stable set polytopes of all graphs. We prove firstly that their Chvátal-rank is at most a, which provides an alternative proof for the validity of clique family inequalities, involving only standard rounding arguments.Secondly, we strengthen the upper bound further and discuss consequences regarding the Chvátal-rank of subclasses of claw-free graphs.


Given a graph G = (V,E) and a “cost function” $f: 2^V\rightarrow\mathbb{R}$ (provided by an oracle), the problem [PCliqW] consists in finding a partition into cliques of V(G) of minimum cost. Here, the cost of a partition is the sum of the costs of the cliques in the partition.We provide a polynomial time dynamic program for the case where G is an interval graph and f belongs to a subclass of submodular set functions, which we call “value-polymatroidal”.This provides a common solution for various generalizations of the coloringproblem in co-interval graphs such as max-coloring,“Greene-Kleitman's dual”, probabilist coloring and chromatic entropy. In the last two cases, this is the first polytime algorithm for co-interval graphs. In contrast, NP-hardness of related problems is discussed. We also describe an ILP formulation for [PCliqW] which gives a common polyhedral framework to express min-max relations such as ${\overline{\chi}}=\alpha$ for perfect graphs and the polymatroid intersection theorem. This approach allows to provide a min-max formula for [PCliqW] if G is the line-graph of a bipartite graph and f is submodular.However, this approach fails to provide a min-max relation for [PCliqW] if G is an interval graphs and f is value-polymatroidal.