Convex programs with an additional constraint on the product of several convex functions

In this paper, we consider a special type of global optimization problem in which a convex function is minimized on X∩Y, where X is a convex set and Y is a nonconvex set represented in terms of a product of p convex functions. It is shown that this problem can be reduced to a p-dimensional reverse convex program. Two outer approximation algorithms are proposed for solving the resulting problem. Computational experiments indicate that these algorithms can generate ϵ-optimal solutions of fairly large scale linear programs with a constraint on the product of up to 4 linear functions.