Generalized Benders Decomposition Method to Solve Big Mixed-Integer Nonlinear Optimization Problems with Convex Objective and Constraints Functions

Abstract

The paper presents the Generalized Benders Decomposition (GBD) method, which is now one of the basic approaches to solve big mixed-integer nonlinear optimization problems. It concentrates on the basic formulation with convex objectives and constraints functions. Apart from the classical projection and representation theorems, a unified formulation of the master problem with nonlinear and linear cuts will be given. For the latter case the most effective and, at the same time, easy to implement computational algorithms will be pointed out.

Keywords

• optimization
• mixed-integer nonlinear programming
• decomposition
• convex problems
• bilinear problems
• integer programming