The Approximate Global Optimal Solution for Some Constrained Programming Problems

Abstract Firstly, convert a programming problem with multiple constraints into a programming problem with single constraint, Secondly, several convexification and concavification transformations for the constrained problem with strictly monotone constraint functions are proposed according to the transformed problem with single constraint, then this constrained programming problem can be converted into a concave minimization or a reverse convex programming problem. Finally, prove that any global optimal solution of the converted concave minimization problem or reverse convex programming problem obtained by the existing algorithms is an approximate global optimal solution of the original problem.