一类具有连续变量的全局最优化问题的凸化方法

摘要

In this paper, we develop convexification approaches and optimization criteria for a general class of nonconvex optimization problem. By using the method of function trans-formations 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.%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。