Nonconvex generalized benders decomposition

Abstract

This chapter gives an overview of an extension of Benders decomposition (BD) and generalized Benders decomposition (GBD) to deterministic global optimization of nonconvex mixed-integer nonlinear programs (MINLPs) in which the complicating variables are binary. The new decomposition method, called nonconvex generalized Benders decomposition (NGBD), is developed based on convex relaxations of nonconvex functions and continuous relaxations of non-complicating binary variables in the problem. NGBD guarantees finding an ε-optimal solution or indicates the infeasibility of the problem in a finite number of steps. A typical application of NGBD is to solve large-scale stochastic MINLPs that cannot be solved via the decomposition procedures of BD and GBD. Case studies of several industrial problems demonstrate the dramatic computational advantage of NGBD over state-of-the-Art commercial solvers.