Résumé
Many convex linearly constrained programs and mixed integer programshave a large number of variables, so that the variables shouldbe generated dynamically throughout the solution algorithm. Thisyields to the well known “branch-and-price algorithm” and “simplicialdecomposition”. We present a novel “branch-and-cut-and-pricealgorithm” to extend this idea to certain classes of convex linearly constrainedMINLP. Our algorithm incorporates the variables generationinto the “LP/NLP algorithm” introduced by Quesada and Grossman.We detail our framework for the stochastic network design problemwith simple recourse and present preliminary computational results.Keywords: convex MINLP, branch-and-price, stochastic programming,network design.