An approximate method for local optima for nonlinear mixed integer programming problems

For a nonlinear 0-1 integer programming problem with constraint set X = (x_{1, ...}x_n), we first add new constraints ∑ 1 n(x_i-x_i ²){approaches the limit}O and O ≤ x_i ≤ 1 to the constraint set, thus to convert the integer problem into a nonlinear programming problem. Then we utilize a modified penalty function method to solve this nonlinear program to obtain a local optima. Running the proposed method by a widely commercialized nonlinear program software shows that this method is more convenient than current approaches as branch-and-bound method and implicit enumeration method. One issue remained for studies is to expand this method into a global method by systematically generating suitable starting points then to perform optimization processes from each of these points.