In this paper, we present an Uzawa-based heuristic that is adapted to certain type of stochastic optimal control problems. More precisely, we consider dynamical systems that can be divided into small-scale subsystems linked through a static almost sure coupling constraint at each time step. This type of problem is common in production/portfolio management where subsystems are, for instance, power units, and one has to supply a stochastic power demand at each time step. We outline the framework of our approach and present promising numerical results on a simplified power management problem.

Recently, [Y.Q. Bai, M. El Ghami and C. Roos,SIAM J. Opt. 15 (2004) 101–128]investigated a new class of kernel functions which differs from theclass of self-regular kernel functions. The class is defined by somesimple conditions on the growth and the barrier behavior of thekernel function. In this paper we generalize theanalysis presented in the above paper for P * (κ) LinearComplementarity Problems (LCPs). The analysis for LCPs deviates significantly from the analysisfor linear optimization. Several new tools and techniques are derived in this paper.

La finance de marché est devenue un des domaines d'ap- plication privilégiés de la recherche opérationnelle. D'un autrecôté, rares sont les applications touchant la banque de détail, tournée vers le grand public. Dans ce papier, nousabordons un problème d'actualité dans le secteur bancaire français : l'optimisation de plans de financementimmobiliers. Le travail que nous présentons a été effectué dans le cadre du développement par la sociétéExperian-Prologia d'une nouvelle application d'instruction de prêts immobiliers pour une grande banque française. Notremodule d'optimisation, au cœur de cette application, est aujourd'hui déployé dans les 2200 agences de cette banqueet permet la simulation et le montage de plusieurs milliers de plans de financement immobiliers chaque mois.

The partial inverse minimum cut problem is to minimally modify the capacities of a digraph such that there exists a minimum cut with respect to the new capacities that contains all arcs of a prespecified set. Orlin showed that the problem is strongly NP-hard if the amount of modification is measured by the weighted L 1-norm. We prove that the problem remains hard for the unweighted case and show that theNP-hardness proof of Yang [RAIRO-Oper. Res.35 (2001) 117–126] for this problem with additionalbound constraints is notcorrect.

In this paper we propose a primal-dual interior-point algorithm forconvex quadratic semidefinite optimization problem. The searchdirection of algorithm is defined in terms of a matrix function andthe iteration is generated by full-Newton step. Furthermore, wederive the iteration bound for the algorithm with small-updatemethod, namely, O( $\sqrt{n}$ log $\frac{n}{\varepsilon}$ ), which isbest-known bound so far.