Decomposition algorithms exploit the structure of large-scale optimization problems by breaking them into a set of smaller subproblems and a coordinating master problem. Cutting-plane methods have been extensively used to decompose convex problems. In this paper, however, we focus on certain nonconvex problems arising in engineering. Engineers have been using bilevel decomposition algorithms to tackle these problems. These algorithms use nonlinear optimization techniques to solve both the master problem and the subproblems. In this paper, we propose two new bilevel decomposition algorithms and show that they converge locally at a superlinear rate. Our computational experiments illustrate the numerical performance of the algorithms.
London Business School working paper 2001