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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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참고문헌 (20)
참고문헌 신청
A. Beck / 2009 / Duality in robust optimization: primal worst equals dual best / Oper. Res. Lett 37 (1) : 1 ~ 6
A. Ben-Tal / 2002 / Robust optimization methodology and applications / Math. Program 92 (3, Ser B) : 453 ~ 480
A. Ben-Tal / 2008 / Selected topics in robust convex optimization / Math. Program 112 (1, Ser. B) : 125 ~ 158
A. Ben-Tal / 2009 / Robust Optimization / Princeton Series in Applied Mathematics
D. Bertsimas / 2004 / Robust linear optimization under general norms / Oper. Res. Lett 32 (6) : 510 ~ 516
A. Ben-Tal / 2002 / Robust optimization methodology and applications / Math. Program 92 (3, Ser B) : 453 ~ 480
A. Ben-Tal / 2008 / Selected topics in robust convex optimization / Math. Program 112 (1, Ser. B) : 125 ~ 158
A. Ben-Tal / 2009 / Robust Optimization / Princeton Series in Applied Mathematics
D. Bertsimas / 2004 / Robust linear optimization under general norms / Oper. Res. Lett 32 (6) : 510 ~ 516
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