A Cutting Plane Algorithm for Linear Reverse Convex Programs

In this paper, global optimization of linear programs with an additional reverse convex constraint is considered. This type of problems arises in many applications such as engineering design, communications network, and many management decision support systems with budget constraints and economies-of-scale. The main difficulty with this type of problem is the presence of the complicated reverse convex constraint, which destroys the convexity and possibly the connectivity of the feasible region, putting the problems in a class of difficult and mathematically intractable problems. The authors present a cutting plane method within the scope of a branch-and-bound scheme that efficiently partitions the polytope associated with the linear constraints and systematically fathoms these portions through the use of the bounds. An upper bound and a lower bound for the optimal value is found and improved at each iteration. The algorithm terminates when all the generated subdivisions have been fathomed.