A simplicial branch and bound duality-bounds algorithm to linear multiplicative programming

A simplicial branch and bound duality-bounds algorithm is presented to globally solving the linear multiplicative programming (lmp). we firstly convert the problem (lmp) into an equivalent programming one by introducing p auxiliary variables. during the branch and bound search,the required lower bounds are computed by solving ordinary linear programming problems derived by using a lagrangian duality theory. the proposed algorithm proves that it is convergent to a global minimum through the solutions to a series of linear programming problems. some examples are given to illustrate the feasibility of the present algorithm. © 2013 xue-gang zhou and bing-yuan cao.