A new linearization technique for minimax linear fractional programming

Abstract

This paper presents a deterministic global optimization algorithm for solving minimax linear fractional programming (MLFP). In this algorithm, a new linearization technique is proposed, which uses more information of the objective function of the (MLFP) than other techniques. By utilizing this new linearization technique, the initial nonconvex programming problem (MLFP) is reduced to a sequence of linear relaxation programming (LRP) problems, which can provide reliable lower bound of the optimal value. The proposed algorithm is convergent to the global minimum of the (MLFP) through the successive refinement of the feasible region and solutions of a series of the (LRP). Compared with the known algorithms, numerical results show that the proposed algorithm is robust and effective.

Keywords:

• global optimization
• minimax linear fractional programming
• linearization technique
• branch-and-bound
• linear relaxation programming

2010 AMS Subject Classifications::

• 90C30
• 90C32
• 65K05

Acknowledgements

This paper is supported by the National Natural Science Foundation of China under Grant (61373174) and the Key Technology Projects of Henan Province (122102110038).