非凸全局最优化的一种凸化、凹化方法

摘要

A strictly monotone function had been converted into a convex or a concave function by the convexification or concavification transformations. If the constraint functions all are decreasing, then the objective function which is neither monotone convex nor concave can be converted into a convex and a concave function by the convexification and concavification transformations. Finally, the original problem was converted into concave minimization or reverse convex programming problem and its global optimal solution was obtained by studying the concave minimization or reverse convex programming problem.%给出了一种凸化、凹化变换，将一个严格单调函数转化为一个凸或凹的函数；给出了一种凸化和凹化变换，在约束函数都是单调递减时，将一个既不单调凸也不是单调凹的目标函数转化为一个凸和凹函数；最终，将原始问题转换成一个凹极小问题或反凸规划问题来求得其最优解．