A Nonmonotone Smoothing Newton Algorithm For Solving Zero-one Nonlinear Integer Programming Problems

We continue the one-zero integer programming problem and reform it to be a nonlinear program.The continuated one-zero integer programming problem is a mathematical program with complementarity constraints(MPCCs), and we obtain an approx-imate solution of the formar problem by solving the latter one. The idea used in this paper is some what different from the existing smoothing methods for MPCCs. We reformulate the MPCC as a system of smoothing equations and use a Newton-type method to solve the resulting system. In order to find out globally optimal solution more effectively, a non-monotone linea search scheme is used in our algorithm.Under some reasonable conditions, the proposed algorithm is shown to be globally and locally superlinearly convergent, and to generate a B-stationary point of the MPCC. Preliminary numerical results for some problems are reported, These results show that the proposed algorithm is effective, what's more, this algorithm for certain examples can gets much better results than existed global optimal results.