The Karush–Kuhn–Tucker optimality conditions in an optimization problem with interval-valued objective function

The Karush–Kuhn–Tucker optimality conditions in an optimization problem with interval-valued objective function

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Article ID: iaor20084730
Country: Netherlands
Volume: 176
Issue: 1
Start Page Number: 46
End Page Number: 59
Publication Date: Jan 2007
Journal: European Journal of Operational Research
Authors:
Keywords: Interval-valued
Abstract:

The KKT conditions in an optimization problem with interval-valued objective function are derived in this paper. Two solution concepts of this optimization problem are proposed by considering two partial orderings on the set of all closed intervals. In order to consider the differentiation of an interval-valued function, we invoke the Hausdorff metric to define the distance between two closed intervals and the Hukuhara difference to define the difference of two closed intervals. Under these settings, we derive the KKT optimality conditions.

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