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

For a nonlinear 0-1 integer programming problem with constraint set , new constraints and are first added to the constraint set, thus to convert the integer problem into a nonlinear programming problem. Then a modified penalty function method is utilized 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.