Smoothing Methods for Nonlinear Complementarity Problems

International audienceIn this paper, we present a new smoothing approach to solve general nonlinear complementarity problems. Under the P0 condition on the original problems, we prove some existence and convergence results . We also present an error estimate under a new and general monotonicity condition. The numerical tests confirm the efficiency of our proposed methods

An exact penalty approach for mathematical programs with equilibrium constraints.

This paper presents an exact penalty approach to solve the mathematical problems with equilibrium constraints (MPECs). This work is based on the smoothing functions introduced in [3] but it does not need any complicate updating rule for the smoothing or penalty parameters. Some numerical academic experiments are carried out to show the efficiency and robustness of this new approach. Two generic applications are also considered: the binary quadratic programs and simple number partitioning problems

Explicit formulas for C1,1C^{1,1} Glaeser-Whitney extensions of 1-fields in Hilbert spaces

We give a simple alternative proof for the $C^{1,1}$--convex extension problem which has been introduced and studied by D. Azagra and C. Mudarra [2]. As an application, we obtain an easy constructive proof for the Glaeser-Whitney problem of $C^{1,1}$ extensions on a Hilbert space. In both cases we provide explicit formulae for the extensions. For the Gleaser-Whitney problem the obtained extension is almost minimal, that is, minimal up to a factor $\frac{1+\sqrt{3}}{2}$ in the sense of Le Gruyer [15]

A Generalized Direction in Interior Point Method for Monotone Linear Complementarity Problems

International audienceIn this paper, we present a new interior point method with full Newton step for monotone linear complementarity problems. The specificity of our method is to compute the Newton step using a modified system similar to that introduced by Darvay in 2003. We prove that this new method possesses the best known upper bound complexity for these methods. Moreover, we extend results known in the literature since we consider a general family of smooth concave functions in the Newton system instead of the square root. Some computational results are included to illustrate the validity of the proposed algorithm

A regularization method for ill-posed bilevel optimization problems

We present a regularization method to approach a solution of the pessimistic formulation of ill -posed bilevel problems . This allows to overcome the difficulty arising from the non uniqueness of the lower level problems solutions and responses. We prove existence of approximated solutions, give convergence result using Hoffman-like assumptions. We end with objective value error estimates.Comment: 19 page

Asymptotic Analysis of Congested Communication Networks

Projet PROMATHThis paper is devoted to the study of a routing problem in telecommunication networks, when the cost function is the average delay. We establish asymptotic expansions for the value function and solutions in the vicinity of a congested nominal problem. The study is strongly related to the one of a partial inverse barrier method for linear programming

Interior Point Methods With Decomposition For Multicommodity Flow Problems

Projet MOCOAThis paper introduces an approach by decomposition of an interior point method for solving multicommodity flow problems. First, we present this approach in the general framework of coupling constraints problems. Next, we propose to specialize the algorithm to the linear multicommodity network-fl- ow problems. We expose this specialization using the node-arc formulation. Then, we focus on the arc-path formulation and we propose decomposition method witch incorporates the interior point method into the Dantzig-Wolfe decomposition technique. The numerical results show the superiority of this last formulation. Finally, we report some numerical results obtained by testing these algorithms with data from the France-Telecom Paris district transmission network