A subdivisional scheme for linear programs with an additional reverse convex constraint

In this paper, global optimization of linear programs with an additional reverse convex program is considered. This type of problem arises in many real world applications such as certain engineering design problems, communications networks, and many management decision support systems, particularly those with budget constraints and economies of scale. The main difficulty with the problem is the presence of the extra reverse convex constraint which destroys the convexity and possibly the connectivity of the feasible region – putting the problem in a class of difficult and mathematically intractable problems. We propose a subdivision strategy on a cone containing the polyhedral space. An upper bound and a lower bound for the optimal value are found and improved at each iteration. The algorithm terminates when all the generated subdivisions have been fathomed.