Some characterizations of robust optimal solutions for uncertain convex optimization problems |
| |
Authors: | Xiang-Kai Sun Zai-Yun Peng Xiao-Le Guo |
| |
Institution: | 1.College of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing,China;2.College of Mathematics and Statistics,Chongqing JiaoTong University,Chongqing,China;3.School of Economics,Southwest University of Political Science and Law,Chongqing,China;4.College of Automation,Chongqing University,Chongqing,China |
| |
Abstract: | In this paper, we consider robust optimal solutions for a convex optimization problem in the face of data uncertainty both in the objective and constraints. By using the properties of the subdifferential sum formulae, we first introduce a robust-type subdifferential constraint qualification, and then obtain some completely characterizations of the robust optimal solution of this uncertain convex optimization problem. We also investigate Wolfe type robust duality between the uncertain convex optimization problem and its uncertain dual problem by proving duality between the deterministic robust counterpart of the primal model and the optimistic counterpart of its dual problem. Moreover, we show that our results encompass as special cases some optimization problems considered in the recent literature. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|