一些类型的数学规划问题的全局最优解

摘要

In this paper, several convexification and concavification transformations for strictly monotone functions are proposed, then a strictly monotone programming problem can be converted into an equivalent canonical D.C. programming problem or concave minimization problem. Furthermore, several convexification and concavification transformations for non-monotone programming problems with single constraint in which objective function is not monotone and constraint function is strictly monotone are proposed too, then the primal programming problem with single strictly monotone constraint function can be converted into an equivalent concave minimization problem. Then the global optimal solution of the primal programming problem can be obtained by solving the converted D.C.programming problem or concave minimization problem via using the existing algorithms.%本文对严格单调函数给出了几个凸化和凹化的方法,利用这些方法可将一个严格单调的规划问题转化为一个等价的标准D.C.规划或凹极小问题.本文还对只有一个严格单调的约束的非单调规划问题给出了目标函数的一个凸化和凹化方法,利用这些方法可将只有一个严格单调约束的非单调规划问题转化为一个等价的凹极小问题.再利用已有的关于D.C.规划和凹极小的算法,可以求得原问题的全局最优解.