We introduce augmented Lagrangian methods for solving finite dimensional variational inequality problemswhose feasible sets are defined by convex inequalities, generalizing the proximal augmented Lagrangian methodfor constrained optimization. At each iteration, primal variables are updated by solvingan unconstrained variational inequality problem, and then dual variables are updated through a closed formula.A full convergence analysis is provided, allowing for inexact solution of the subproblems.

We consider the maximum weight perfectly matchable subgraph problemon a bipartite graph G=(UV,E) with respect to given nonnegativeweights of its edges. We show that G has a perfect matching if andonly if some vector indexed by the nodes in UV is a base of anextended polymatroid associated with a submodular function definedon the subsets of UV. The dual problem of the separation problemfor the extended polymatroid is transformed to the special maximumflow problem on G. In this paper, we give a linear programmingformulation for the maximum weight perfectly matchable subgraphproblem and propose an O(n 3) algorithm to solve it.

We discuss the problem of computing points of IR n whoseconvex hull contains the Euclidean ball, and is containedin a small multiple of it. Given a polytope containing the Euclidean ball, we introduce its successor obtained by intersectionwith all tangent spaces to the Euclidean ball, whose normalspoint towards the vertices of the polytope. Starting from the L ∞ ball,we discuss the computation of the two first successors, andgive a complete analysis in the case when n=6.

This paper considers the problem of scheduling n jobs on a single machine. A fixed processing time and an execution interval are associated with each job. Preemption is not allowed. On the basis of analytical and numerical dominance conditions, an efficient integer linear programming formulation is proposed for this problem, aiming at minimizing the maximum lateness (L max). Experiments have been performed by means of a commercial solver that show that this formulation iseffective on large problem instances. A comparison with thebranch-and-bound procedure of Carlier is provided.

Let G = (V,E) be a simple undirected graph.A forest F ⊆ E of G is said to be clique-connecting if each tree of F spans a clique of G.This paper adresses the clique-connecting forest polytope.First we give a formulation and a polynomial time separation algorithm. Then we show that the nontrivial nondegenerate facets of the stable set polytope are facets of the clique-connecting polytope.Finally we introduce a family of rank inequalities which are facets, and which generalize the clique inequalities.

In the last decade, the authorities require the use of safe, comfortable vehicles to assure a door to door aspect with respect of environment in the urban context. In this paper, we propose an advanced approach of transport regulation where we integrate cybercars into a regulation process as an alternative in disruption cases. For that, we propose an ITS architecture including public transportation and cybercars into the same framework. We will show that collaboration between these two systems provides better results than managing them separably.