https://enpc.hal.science/hal-03542218Forcier, MaëlMaëlForcierENPC - École des Ponts ParisTechTROPICAL - TROPICAL - CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique - Inria Saclay - Ile de France - Inria - Institut National de Recherche en Informatique et en AutomatiqueLeclère, VincentVincentLeclèreENPC - École des Ponts ParisTechGeneralized adaptive partition-based method for two-stage stochastic linear programs : convergence and generalizationHAL CCSD2022[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Forcier, Maël2022-01-25 11:15:042023-03-24 14:53:252022-05-12 10:37:25enPreprints, Working Papers, ...1Adaptive Partition-based Methods (APM) are numerical methods to solve two-stage stochastic linear problems (2SLP). The core idea is to iteratively construct an adapted partition of the space of alea in order to aggregate scenarios while conserving the true value of the cost-to-go for the current first-stage control. Relying on the normal fan of the dual admissible set, we extend the classical and generalized APM method by i) extending the method to almost arbitrary 2SLP, ii) giving a necessary and sufficient condition for a partition to be adapted even for non-finite distribution, and iii) proving the convergence of the method. We give some additional insights by linking APM to the L-shaped algorithm.