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Optimality conditions in multiobjective programming problems with interval valued objective functions

Ahmad I., Singh D., Dar B. A.

Control and Cybernetics

2015

Vol. 44, no. 1

19--45

We devote this paper to study of multiobjective programming problems with interval valued objective functions. For this, we consider two order relations LU and LS on the set of all closed intervals and propose several concepts of Pareto optimal solutions and generalized convexity. Based on generalized convexity (viz. LU and LS-pseudoconvexity) and generalized diﬀerentiability (viz. gHdiﬀerentiablity) of interval valued functions, the KKT optimality conditions for aforesaid problems are obtained. The theoretical development is illustrated by suitable examples.