单调优化的一种新凸化和凹化方法

A New Convexification and Concavification Method for Monotone Optimization

提出了一个新的凸化、凹化变换,并证明了单调非线性规划总能变换成相应的凹极小化问题或反凸规划或标准D.C规划问题,再利用已有的关于这些规划问题求全局最优解的方法,可以求得原问题的全局最优解.

This paper proposes a new convexfifcation or coneavification transformation method to convert a monotone into a convex or concave function. Then the monotone optimization problem can be converted into an equivalent concave minimization problem or reverse convex programming problem or canonic D. C programming problem. Therefore, the global minimizer of the original programming problem can be obtained by the existing algorithms about the converted structured problems.