In this paper, a new outer space rectangle branch and bound algorithm is proposed for globally solving generalized affine multiplicative programming problem. By applying the equivalent transformations and affine approximations of bilinear function, the initial generalized affine multiplicative programming problem can be reduced to a linear relaxed programming problem. By subsequently refine the initial outer space rectangle, and by means of the subsequent solutions of a series of linear relaxed programming problems, the algorithm is convergent to the global optimal solution of the primal problem, and numerical results show the feasibility and effectiveness of the algorithm. INDEX TERMS Generalized affine multiplicative programming, global optimization, linear relaxed programming, branch and bound.

No abstract

No abstract

Base on the outer space search and the branch-and-bound framework, this paper presents an efficient outer space branch-and-bound algorithm for globally solving generalized linear multiplicative programming problem. First of all, we convert the problem into an equivalent problem. Then, by utilizing a direct relaxation method, we establish the linear relaxed problem to compute the lower bound of the global optimal value of the equivalent problem. By subsequently subdividing the initial outer space rectangle and solving a series of linear relaxed problems, the proposed algorithm is convergent to the global optimal solution of the primal problem. Finally, compared with some known algorithms, numerical experiments are given to demonstrate the feasibility and effectiveness of the proposed algorithm. INDEX TERMS Generalized linear multiplicative programming problem, global optimization, linear relaxed problem, branch-and-bound algorithm.