Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications

We study sample approximations of chance constrained problems. In particular, we consider the sample average approximation (SAA) approach and discuss the convergence properties of the resulting problem. We discuss how one can use the SAA method to obtain good candidate solutions for chance constrained ( )Departamento de Matemática, Pontif́ıcia Universidade Católica do Rio de Janeiro, Rio de Janeiro, RJ Brazil 22453-900, e-mail: [email protected], research supported by CAPES and FUNENSEG. Georgia Institute of Technology, Atlanta, Georgia 30332, USA, e-mail: [email protected], research of this author was partly supported by the NSF award DMI-0133943. Georgia Institute of Technology, Atlanta, Georgia 30332, USA, e-mail: [email protected], research of this author was partly supported by the NSF award DMI-0619977. 1 problems. Numerical experiments are performed to correctly tune the parameters involved in the SAA. In addition, we present a method for constructing statistical lower bounds for the optimal value of the considered problem and discuss how one should tune the underlying parameters. We apply the SAA to two chance constrained problems. The first is a linear portfolio selection problem with returns following a multivariate lognormal distribution. The second is a joint chance constrained version of a simple blending problem.