Separable concave minimization via partial outer approximation and branch and bound

Abstract

This paper presents a new algorithm for globally minimizing a separable, concave function over a compact convex set. The algorithm uses partial outer approximation and branch and bound. The major computational effort required is solving linear programming problems at some nodes of the branch and bound tree, and solving simple univariate minimizations in some iterations. The algorithm partially mitigates the rapid growth in the number of constraints of the linear programs that would frequently occur if traditional outer approximation were used. Furthermore, unlike outer approximation, the algorithm does not explicitly construct polyhedra which contain the feasible region.