In collaboration with Payame Noor University and the Iranian Society of Instrumentation and Control Engineers

Document Type : Research Article


Department of Mathematics‎, ‎Payame Noor University (PNU)‎,‎ P.O‎. ‎Box 19395-4697‎, ‎Tehran‎, ‎Iran‎.


This paper aims to establish first-order necessary optimality conditions for non-smooth multi-objective generalized semi-infinite programming problems‎. ‎These problems involve inequality constraints whose index set depends on the decision vector‎, ‎and all emerging functions are assumed to be locally Lipschitz‎. ‎We introduce a new constraint qualification for these problems‎. ‎Building upon this qualification‎, ‎we derive an upper estimate for the Clarke sub-differential of the value function of the problem‎. ‎Furthermore‎, ‎we demonstrate the necessary optimality conditions for properly efficient solutions to the problem‎.


Main Subjects

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