Approximate Karush‐Kuhn‐Tucker Condition in Multiobjective Optimization

We extend the so‐called approximate Karush–Kuhn–Tucker condition from a scalar optimization problem with equality and inequality constraints to a multiobjective optimization problem. We prove that this condition is necessary for a point to be a local weak efficient solution without any constraint qualification, and is also sufficient under convexity assumptions. We also state that an enhanced Fritz John‐type condition is also necessary for local weak efficiency, and under the additional quasi‐normality constraint qualification becomes an enhanced Karush–Kuhn–Tucker condition. Finally, we study some relations between these concepts and the notion of bounded approximate Karush–Kuhn–Tucker condition, which is introduced in this paper.