Generalized cutting plane method for solving nonlinear stochastic programming problems

摘要

A tiny subclass of minimum-type functions, called , is introduced. We show that abstract convex functions generated by and those generated by the whole class of minimum-type functions coincide. Other concepts from abstract convex analysis such as support set, subdifferential and conjugate function with respect to are investigated. We will use these results to establish a stochastic version of generalized cutting plane method (SGCPM) to solve two-stage nonconvex programming problems. Under mild conditions, we will show that every limit point of the sequence generated by SGCPM is an optimal solution.