A resource constraint approach for one global constraint minlp

Abstract

Many industrial optimization problems are sparse and can be formulated as block-separable mixed-integer nonlinear programming (MINLP) problems, where low-dimensional sub-problems are linked by a (linear) knapsack-like coupling constraint. This paper investigates exploiting this structure using decomposition and a resource constraint formulation of the problem. The idea is that one outer approximation master problem handles sub-problems that can be solved in parallel. The steps of the algorithm are illustrated with numerical examples which shows that convergence to the optimal solution requires a few steps of solving sub-problems in lower dimension.