Higher-order conditions for strict efficiency revisited

D. V. Luu and P. T. Kien propose in Soochow J. Math. 33 (2007), 17-31, higher-order conditions for strict efficiency of vector optimization problems based on the derivatives introduced by I. Ginchev in Optimization 51 (2002), 47-72. These derivatives are defined for scalar functions and in their terms necessary and sufficient conditions can be obtained a point to be strictly efficient (isolated) minimizer of a given order for quite arbitrary scalar function. Passing to vector functions, Luu and Kien lose the peculiarity that the optimality conditions work with arbitrary functions. In the present paper, applying the mentioned derivatives for the scalarized problem and restoring the original idea, optimality conditions for strictly efficiency of a given order are proposed, which work with quite arbitrary vector functions. It is shown that the results of Luu and Kien are corollaries of the given conditions. Key words: nonsmooth vector optimization, higher-order optimality conditions, strict efficiency, isolated minimizers.