A one-dimensional branching rule based branch-and-bound algorithm for minimax linear fractional programming

This paper investigates a type of minimax linear fractional program (MLFP) that often occurs in practical problems such as design of electronic circuits, finance and investment. We first transform the MLFP problem into an equivalent problem (EP) by using the Charnes-Cooper transformation and introducing an auxiliary variable. A linear relaxation strategy should simplify the nonconvex parts of the constraints in (EP). For globally solving MLFP, a branch-and-bound algorithm is then developed. It integrates the presented relaxation with the one-dimensional branching. The convergence of the algorithm is demonstrated and the number of worst-case iterations is estimated. Finally, preliminary numerical experiments verify that the proposed algorithm in this article is robust and efficient for solving the tested instances.