On the approximation of real rational functions via mixed-integer linear programming

Abstract

This paper is introducing a new method for the approximation of real rational functions via mixed-integer linear programming. The formulation of the linear approximation problem is based on the minimization of a suitable minimax criterion, in combination with a branch and bound linear integer technique. The proposed algorithm can be used in many rational approximation problems, where some coefficients of the rational function are required to take only integer values. The formulation of the problem ensures always the global solution. The proposed algorithm was extensively tested on a variety of problems. An analytical example is presented to illustrate the use and effectiveness of the algorithm.