Alireza Mohebi Ashtiani - Academic Department of Mathematics, Parana Federal University of Technology (UTFPR),Londrina, PR, Brazil
Thiago Fernando Kawakami - Academic Department of Mechanical Engineering, Parana Federal University of Technology (UTFPR),Londrina, PR, Brazil

This paper presents an approach for globally solving the problem of minimizing a product of two finite positive linear functions. Since the product of linear functions need not be convex or quasi-convex thus the given problem may have many local minima which are not a global minimum. The original problem is first reformulated as an equivalent indefinite quadratic problem, then solved through a rectangular branch-and-bound procedure. The computational experiences show the robustness and efficiency of the proposed algorithm.

Global optimization, Branch-and-Bound, Nonconvex optimization