First and second order optimality conditions in vector optimization

Abstract In this paper we suggest a general approach in studying optimality for a multiobjective problem. First and second order optimality conditions are firstly achieved by means of suitable tangent sets; the obtained results are specified for an unconstrained problem and for a problem whose feasible region is expressed by means of functional constraints. Furthermore, the role played by generalized concavity and by second order regularity conditions is pointed out in order to achieve first order sufficient optimality condìtìons and in order to obtain second order optimality conditions in a dual form involving multipliers, respectively.

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