A parametric successive underestimation method for convex programming problems with an additional convex multiplicative constraint

This paper addresses itself to an algorithm for a convex minimization probelm with an additional convex multiplicative constraint. A convex multiplicative constraint is such that a product of two convex functions is less than or equal to some constant. It is shown that this nonconvex problem can be solved by solving a sequence of convex programming problems. The basic idea of this algorithm is to embed the original problem into a problem in a higher dimensional space and to apply a parametric programming technique. A branch-and-bound algorithm is proposed for obtaining an ∈-optimal solution in finitely many iterations. Computational results indicate that this algorithm is efficient for linear programs with an additional linear multiplicative constraint.