Globally minimizing a class of linear multiplicative forms via simplicial branch-and-bound

We consider in this paper a class of linear multiplicative programming problems that arise from numerous applications such as network flows and financial optimization. The problem is first transformed into an equivalent nonlinear optimization problem to provide a novel convex quadratic relaxation. A simplicial branch-and-bound algorithm is then designed to globally solve the problem, based on the proposed relaxation and simplicial branching process. The convergence and computational complexity of the algorithm are also analyzed. The results of numerical experiments confirm the efficiency of the proposed algorithm for tested instances.