A deterministic approach to linear programs with several additional multiplicative constraints

We consider a global optimization problem of minimizing a linear function subject to p linear multiplicative constraints as well as ordinary linear constraints. We show that this problem can reduce to a 2p-dimensional reverse convex program, and present an algorithm for solving the resulting problem. Our algorithm converges to a globally optimal solution and yields an ε-approximate solution in finite time for any ε > 0. We also report some results of computational experiment.