On Highly Robust Approximate Solutions for Nonsmooth Convex Optimizations with Data Uncertainty
Jutamas Kerdkaew, Rabian Wangkeeree, Gue Myung Lee
Keywords:
convex optimization problems with uncertain data, robust optimization problems, highly robust solutions, approximate quasi solutions, approximate optimality conditions, approximate dualityAbstract
In this paper, we investigate a convex optimization problem in the face of data uncertainty in both objective and constraint functions. The notion of an ε-quasi highly robust solution (one sort of approximate solutions) for the convex optimization problem with data uncertainty is introduced. The highly robust approximate optimality theorems for ε-quasi highly robust solutions of uncertain convex optimization problem are established by means of a robust optimization approach (worst-case approach). Furthermore, the highly robust approximate duality theorems in terms of Wolfe type on ε-quasi highly robust solutions for the uncertain convex optimization problem are obtained. Moreover, to illustrate the obtained results or support this study, some examples are presented.
