On Highly Robust Approximate Solutions for Nonsmooth Convex Optimizations with Data Uncertainty

Jutamas Kerdkaew, Rabian Wangkeeree, Gue Myung Lee

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  • Support Team

Keywords:

convex optimization problems with uncertain data, robust optimization problems, highly robust solutions, approximate quasi solutions, approximate optimality conditions, approximate duality

Abstract

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.

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Published

2020-09-01

How to Cite

Team, S. (2020). On Highly Robust Approximate Solutions for Nonsmooth Convex Optimizations with Data Uncertainty: Jutamas Kerdkaew, Rabian Wangkeeree, Gue Myung Lee. Thai Journal of Mathematics, 18(3), 977–995. Retrieved from https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1051

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