Global optimization for special reverse convex programming

A global optimization algorithm is proposed in order to locate the global minimum of the special reverse convex programming which is both nonconvex and nonlinear. Three new strategies are adopted in this paper. Some of them can be used to solve general reverse convex programming. Global solution locating is to identify the location of the solution. The linear relaxation method is used to obtain the lower bound of the optimum of the primal programming, and in this paper the relaxed programming is a kind of linear programming, which can be solved by standard simplex algorithm. The final strategy is upper bound updating method, which provides a better upper bound than the standard branch and bound method. According to the strategies, a global optimization algorithm is derived based on branch and bound theory. It is proved that the algorithm possesses global convergence. Finally, a numerical experiment is given to illustrate the feasibility and the smaller computational effort.