Abstract
In this paper, strong Karush/Kuhn–Tucker conditions are studied for smooth multiobjective optimization with inequality constraints. We introduce a new second-order regularity condition of Abadie type in terms of the second-order directional derivatives and then obtain a second-order strong Karush/Kuhn–Tucker necessary condition at a Borwein-properly efficient solution. Simultaneously, we also use an example to show that, if the Abadie type regularity condition is weakened to the Guignard type one, the second-order strong Karush/Kuhn–Tucker necessary condition may not hold. Finally, then we also apply the second-order strong Karush/Kuhn–Tucker conditions to derive a sufficient result for local Geoffrion-proper efficiency.
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