ON NONSMOOTH OPTIMALITY THEOREMS FOR ROBUST OPTIMIZATION PROBLEMS

• Lee, Gue Myung (Department of Applied Mathematics Pukyong National University) ;
• Son, Pham Tien (Center of Research and Development Duy Tan University, Department of Mathematics University of Dalat)
• Received : 2013.04.01
• Published : 2014.01.31

Abstract

In this paper, we prove a necessary optimality theorem for a nonsmooth optimization problem in the face of data uncertainty, which is called a robust optimization problem. Recently, the robust optimization problems have been intensively studied by many authors. Moreover, we give examples showing that the convexity of the uncertain sets and the concavity of the constraint functions are essential in the optimality theorem. We present an example illustrating that our main assumptions in the optimality theorem can be weakened.

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