Outer space branch-reduction-bound algorithm for solving generalized affine multiplicative problems

This paper presents an outer space branch-reduction-bound algorithm for globally solving generalized affine multiplicative problems (GAMP). For finding the globally optimal solution to the GAMP, we first transform the GAMP into an equivalent problem (EP) by introducing new variables and logarithmic transformation. Next, by utilizing linearization technique of logarithmic function, the affine relaxation problem of the EP can be established for obtaining the lower bound of the optimal value to the EP. Furthermore, several outer space region reduction techniques are also presented for improving the convergence speed of this algorithm. Based on outer space search and branch-and-bound framework, a branch-reduction-bound algorithm is proposed. Finally, we prove the global convergence of the proposed algorithm, and estimate maximum iterations by analyzing its computational complexity. Some experiments are reported to show the feasibility and efficiency of the algorithm. (c) 2022 Elsevier B.V. All rights reserved.