Output-space branch-and-bound reduction algorithm for generalized linear fractional-multiplicative programming problem

Abstract

In this paper, we investigate a class of linear fractional-multiplicative programs with exponents, which have important applications in finance and economy. By introducing p variables, the problem is re-represented as an equivalent problem. Immediately, two new linear relaxation strategies are proposed and embedded in the branch-and-bound framework, and the corresponding new global optimization algorithms are developed in combination with an acceleration technique. Furthermore, the theoretical convergence and computational complexity of the algorithms are elucidated. Numerical experiment results illustrate that both algorithms are effective and feasible.