This paper presents a fusion of Stochastic Decomposition and the Majorization-Minimization algorithm (SD-MM) to solve a class of non-convex stochastic programs. The objective function is an expectation of a smooth concave function and a second-stage linear recourse function, which is common in stochastic programming (SP). This extension not only allows new stochastic difference-of-convex (dc) functions but allows new applications in which these two crucial paradigms (SP and dc) can be integrated to provide a more powerful setting for modern applications. This combination also provides an opportunity to study convergence results in a more general setting. Furthermore, with the predictive capability of k nearest neighbors estimation, the proposed algorithm is also extended to solve nonconvex predictive stochastic programming, where the data are present as covariates, and the underlying conditional distribution is unknown. Finally, the computational results of various instances prove the efficiency of the methodology.
Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles CA, 90089-0193, USA, May 9, 2022