Higher-order strict minimizers with respect to a nonlinear function for a multiobjective optimization problem are introduced and are characterized via sufficient optimality conditions and higher-order mixed saddle points of a vector-valued partial Lagrangian. To this aim, we present certain generalizations of higher-order strong invexity. A mixed dual is proposed and corresponding duality results are obtained. An equivalent optimization problem for the given multiobjective optimization problem is introduced. It is shown that the problem of finding higher-order strict minimizers with respect to a nonlinear function for the given problem reduces to that of finding strict minimizers in the ordinary sense for an equivalent problem. MSC:26A51, 90C29, 90C46.
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