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On \({\epsilon}\) -solutions for convex optimization problems with uncertainty data

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We consider \({\epsilon}\) -solutions (approximate solutions) for a robust convex optimization problem in the face of data uncertainty. Using robust optimization approach (worst-case approach), we establish an optimality theorem and duality theorems for \({\epsilon}\) -solutions for the robust convex optimization problem. Moreover, we give an example illustrating the duality theorems.

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Correspondence to Gue Myung Lee.

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The authors would lies to express their sincere thanks to anonymous referees for variable suggestions and comments for the paper.

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2011-0018619).

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Lee, J.H., Lee, G.M. On \({\epsilon}\) -solutions for convex optimization problems with uncertainty data. Positivity 16, 509–526 (2012).

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