广义凸性下多目标优化

严格凸优化问题在理论上已证明有唯一的全局最优解,并且可应用快速的多项式时间算法和软件求解这一全局最优解。所有的优化问题都体现出凸性,故优化问题的分水岭不是线性与非线性,而是凸性与非凸性[14]。本文叙述了广义凸性下部分研究成果,广义凸函数是凸函数的弱化及推广,它与函数数的作用一样,当目标函数或约束条件是具备某些广义凸性,即拟凸、伪凸,似不变凸等条件时,也能获得多目标规划的最优有效解,相应地也可得到弱对偶和强对偶的一些结果。

Several Problems about the Generalized Convexity

In this article,we will prove that,under the differential condition,the strict pseudo_convexity and Orgega_Rheinbold pseudo_convex are equivalent.What's more,we will discuss the relation between the r_convexity and the analog convexity.