一类具有连续变量的全局最优化问题的凸化方法

CONVEXIFICATION APPROACHES FOR A CLASS OF CONTINUOUS GLOBAL OPTIMIZATION PROBLEM

本文研究了一类非凸最优化问题的凸化方法与最优性条件的问题.利用构造含有参数的函数变换方法,将具有次正定性质的目标函数凸化,并获得了这一类非凸优化问题全局最优解的充要条件,推广了凸化方法在求解全局最优化问题方面的应用.

In this paper,we develop convexification approaches and optimization criteria for a general class of nonconvex optimization problem.By using the method of function transformations with parameter,a class of novel convexification schems is presented for solving global optimization problem with positive sub-definite objective function.The general class of nonconvex programming discussed in the paper can be solved to global optimality,which extends applications of convexification schems in solving global optimization problems.