一类全局优化问题的新的凸化、凹化法

A new method of convexification and concavification for a kind of global optimization

对于目标函数非凸非凹,而约束函数具有凹、凸性的非线性规划问题,本文提出了一种新的凸化凹化法。把目标函数直接凸化、凹化,再把原问题转化为反凸规划问题或极小化问题或标准D.C.规划问题,从而求得原问题的全局最优解。

This paper proposes a kind of convexification and concavification method to convert a non-convex and non-concave objective function into a convex or concave function in the programming problems with convex or concave constraint functions.Then it proves that the original programming problems can be converted into an equivalent concave minimization problem,or reverse convex programming problem,or canonical D.C.programming problem.