A new branch and bound method for solving linear multiplicative programming problems

This paper studies a class of linear multiplicative problems (LMP). To find a global optimal solution of problem (LMP), we first convert problem (LMP) into an equivalent problem (EP) via auxiliary variables, then problem (EP) is expressed as a two-layer problem (EP1). On the basis of problems (EP) and (EP1), a new bounding technique which integrates two linear relaxation processes is proposed to obtain a valid lower bound for the optimal value of (LMP). Combining the bounding technique with the bisection branching rule, a novel branch and bound algorithm is designed. Also, we establish the global convergence of the proposed algorithm and estimate its computational complexity. Preliminary numerical results verify the feasibility and effectiveness of the presented method.