Robust approximate optimal solutions for nonlinear semi-infinite programming with uncertainty. (1st September 2020) - Sun, Xiangkai; Teo, Kok Lay; Zeng, Jing; Liu, Liying
Abstract : In this paper, we deal with robust approximate quasi optimal solutions for a class of nonlinear semi-infinite programming with data uncertainty (USIP) in both the objective and constraints. By using a new robust-type subdifferential constraint qualification and some generalized convexity assumptions, we first establish approximate optimality conditions for robust approximate quasi optimal solutions of (USIP) . Then, we introduce a Mixed-type robust approximate dual problem for (USIP) and investigate robust approximate duality relations between them. Furthermore, we establish a nonsmooth robust approximate saddle point theorem for an uncertain approximate Lagrangian function associated with (USIP) .