Global optimization of convex multiplicative programs by duality theory

A global optimization approach for convex multiplicative problems based on the generalized Benders decomposition is proposed. A suitable representation of the multiplicative problem in the outcome space reduces its global solution to the solution of a sequence of quasi-concave minimizations over polytopes. Some similarities between convex multiplicative and convex multiobjective programming become evident through the methodology proposed. The algorithm is easily implemented; its performance is illustrated by a test problem.