Optimization Letters (2019) 13:657–672 https://doi.org/10.1007/s11590-018-1300-8 ORIGINAL PAPER Partial sample average approximation method for chance constrained problems Jianqiang Cheng 1 · Céline Gicquel 2 · Abdel Lisser 2 Received: 22 September 2017 / Accepted: 19 July 2018 / Published online: 23 July 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract In this paper, we present a new scheme of a sampling-based method to solve chance constrained programs. The main advantage of our approach is that the approxima- tion problem contains only continuous variables whilst the standard sample average approximation (SAA) formulation contains binary variables. Although our approach generates new chance constraints, we show that such constraints are tractable under certain conditions. Moreover, we prove that the proposed approach has the same con- vergence properties as the SAA approach. Finally, numerical experiments show that the proposed approach outperforms the SAA approach on a set of tested instances. Keywords Stochastic programming · Chance constraints · Sampling-based method 1 Introductions In this paper, we focus on the following chance constrained problems: min f (x ) (1a) (CCP ) s .t . p 0 (x ) := P{g j (x ,ξ) ≥ 0, j = 1,..., m}≥ 1 − η (1b) x ∈ X , (1c) B Jianqiang Cheng jqcheng@email.arizona.edu Céline Gicquel celine.gicquel@lri.fr Abdel Lisser lisser@lri.fr 1 Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ 85721, USA 2 Laboratoire de Recherche en Informatique (LRI), Université Paris Sud - XI, Bât. 650, 91405 Orsay Cedex, France 123