An efficient global optimization algorithm for a class of linear multiplicative problems based on convex relaxation

This paper presents an efficient global optimization algorithm to solve a class of linear multiplicative problems (LMP). The algorithm first converts LMP into an equivalent problem (EP) via some variables transformation, and a convex relaxation problem is constructed to derive a lower bound to the optimal value of EP. Consequently, the process of solving LMP is transformed into tackling a series of convex programs. Additionally, a pruning rule is developed to offer a chance to remove the portion of the investigated space which does not contain the optimal solution of EP, and we propose a strategy which provides more choices of the feasible solution to update the upper bound for the optimal value of LMP. We also analyze the convergence of the algorithm and give its complexity result. Finally, our approach has been confirmed to be effective based on numerical results.