Generalized cutting plane method for solving nonlinear stochastic programming problems. (2nd August 2020)

• Record Type: Journal Article
• Authors: Doagooei, Ali Reza
• Is Part Of: Optimization. Volume 69:Number 7/8(2020)
• Page Start: 1751
• Page End: 1771
• Publication Date: 2020-08-02
• Subjects: Generalized convexity -- degree-one calm functions -- minimum-type subgradients -- two-stage nonconvex programming problems -- cutting plane method; 26B25 -- 90C26 -- 90C15; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1711081
• Languages: English
• ISSNs: 0233-1934

Abstract

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.