一类带DC函数的分式优化的Farkas引理刻画

Characterizations of Farkas Lemmas for a Class of Fractional Optimization with DC Functions

该文旨在刻画一类带有DC函数(即两个凸函数的差)的约束分式优化问题的Farkas引理.借助Dinkelbach方法,将该分式优化问题转化为DC优化问题.随后借助共轭函数的上图技巧所引入的新的正则性条件,刻画了该DC优化问题与其Fenchel-Lagrange对偶问题之间的对偶关系,从而建立了该分式优化问题的一些新的Farkas引理,推广和改进了相关文献的结果.

This paper deals with some new Farkas lemmas for a class of constraint fractional optimization with DC functions(the difference of convex functions).Following the idea due to Dinkelbach,we first associate the fractional optimization with a DC optimization problem.Then,by using the epigraph technique of the conjugate function,we introduce some new regularity conditions and establish the duality between the DC optimization problem and its Fenchel-Lagrange dual problem.Finally,we obtain some new Farkas lemmas for the fractional optimization problem.Furthermore,we also show that the results obtained in this paper extend and improve the corresponding results in the literature.