Conical algorithm for the global minimization of linearly constrained decomposable concave minimization problems

In this paper, we are concerned with the linearly constrained global minimization of the sum of a concave function defined on ap-dimensional space and a linear function defined on aq-dimensional space, whereq may be much larger thanp. It is shown that a conical algorithm can be applied in a space of dimensionp + 1 that involves only linear programming subproblems in a space of dimensionp +q + 1. Some computational results are given.This research was accomplished while the second author was a Fellow of the Alexander von Humboldt Foundation, University of Trier, Trier, Germany.