On nonsmooth Optimality theorems for robust optimization problems
Bull. Korean Math. Soc. 2014 Vol. 51, No. 1, 287-301
Printed January 1, 2014
Gue Myung Lee and Ph\d{a}m Ti\ees n S\ow n
Pukyong National University, University of Dalat
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.
Keywords : robust optimization problem, Lagrange multipliers, locally Lipschitz functions, generalized gradients, necessary optimality conditions
MSC numbers : Primary 90C22, 90C25, 90C46
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