Some characterizations of duality for DC optimization with composite functions |
| |
Authors: | Xiangkai Sun Xian-Jun Long Minghua Li |
| |
Affiliation: | 1. National Research Base of Intelligent Manufacturing Service, College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, China.sxkcqu@163.comsunxk@ctbu.edu.cn;4. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, China.;5. School of Mathematics and Finance, Chongqing University of Arts and Sciences, Chongqing, China. |
| |
Abstract: | In this paper, by virtue of the epigraph technique, we first introduce some new regularity conditions and then obtain some complete characterizations of the Fenchel–Lagrange duality and the stable Fenchel–Lagrange duality for a new class of DC optimization involving a composite function. Moreover, we apply the strong and stable strong duality results to obtain some extended (stable) Farkas lemmas and (stable) alternative type theorems for this DC optimization problem. As applications, we obtain the corresponding results for a composed convex optimization problem, a DC optimization problem, and a convex optimization problem with a linear operator, respectively. |
| |
Keywords: | Duality DC optimization composite functions regularity conditions |
|
|