This paper aims at studying, in the image space, an approximation of a vector optimization problem obtained by substituting the involved functions with their G-derivatives. It is shown that, under the hypothesis of G-differentiability, the existence of a semistationary point is equivalent to the linear separation between the image of the approximated problem and a suitable convex subset of the image space. Applications to optimality conditions are provided.
Image Space Analysis and Separation for G-Semidifferentiable Vector Problems
PELLEGRINI, Letizia
2013-01-01
Abstract
This paper aims at studying, in the image space, an approximation of a vector optimization problem obtained by substituting the involved functions with their G-derivatives. It is shown that, under the hypothesis of G-differentiability, the existence of a semistationary point is equivalent to the linear separation between the image of the approximated problem and a suitable convex subset of the image space. Applications to optimality conditions are provided.
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