Fabian Bastin : February 2, 2005

Trust-region approaches for nonlinear stochastic programming and mixed logit models.

Abstract

We consider nonlinear nonconvex stochastic problems, and explore how to exploit their properties in order to develop numerically efficient solving methods. We first examine multistage stochastic nonlinear programs with linear constraints, in the framework of primal-dual interior point methods. We next study consistency of sample average approximations (SAA) for general nonlinear stochastic programs. We also develop a new algorithm to solve the SAA problem, using the statistical inference information to reduce numerical costs by means of an internal variable sample size strategy. We finally assess the numerical efficiency of the proposed method for the estimation of mixed logit models, in the context of discrete choice theory.