Generalized cutting plane method for solving nonlinear stochastic programming problems. (2nd August 2020) - Doagooei, Ali Reza
ABSTRACT: A tiny subclass of minimum-type functions, called G n + 1, is introduced. We show that abstract convex functions generated by G n + 1 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 G n + 1 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.