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

Jutamas Kerdkaew, Rabian Wangkeeree, Gue Myung Lee


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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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|