On Solving Nonsmooth Mixed-Integer Nonlinear Programming Problems by Outer Approximation and Generalized Benders Decomposition

Zhou Wei, M. Montaz Ali, Liang Xu, Bo Zeng, Jen-Chih Yao

Abstract: In this paper, we mainly study nonsmooth mixed-integer nonlinear programming problems and solution algorithms by outer approximation and generalized Benders decomposition. Outer approximation and generalized Benders algorithms are provided to solve these problems with nonsmooth convex functions and with conic constraint, respectively. We illustrate these two algorithms by providing detailed procedure of solving several examples. The numerical examples show that outer approximation and generalized Benders decomposition provide a feasible alternative for solving such problems without differentiability.