Abstract: We propose a new branch and bound reduction algorithm for solving a class of linear multiplicative programming problems with constant coefficients. Firstly, by utilizing the convex envelopes of the products of two variables, the lower and upper bounds for the multiplications in the objective and constraint functions are determined. And we use these bounds to construct the corresponding convex programming relaxation for the original problem. Then, resorting to the hyper-rectangular reduction strategy, a new branch and bound reduction algorithm is designed. It is shown that this new algorithm is globally convergent. Numerical examples are presented to illustrate the effectiveness of the proposed algorithm.

Key words: global optimization, multiplicative constraints, linear multiplicative programming, branch and bound, relaxed programming problem