An algorithm for finding global minimum of nonlinear integer programming

A filled function is proposed by R.Ge for finding a global minimizer of a function of several continuous variables. In [4], an approach for finding a global integer minimizer of nonlinear function using the above filled function is given. Meanwhile a major obstacle is met: if ρ > 0 is small, and || x_I - x^*_I|| is large, where x_I is an integer point, and x^*_I is a current local integer minimizer, then the value of the filled function almost equals zero. Thus it is difficult to recognize the size of the value of the filled function and can not to find the global integer minimizer of nonlinear function. In this paper, two new filled functions are proposed for finding global integer minimizer of nonlinear function, and the new filled function improves some properties of the filled function proposed by R. Ge. Some numerical results are given, which indicate that the new filled function (4.1) to find global integer minimizer of nonlinear function is efficient.