Copyright © 2010 Ying Gao et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study first- and second-order necessary and sufficient optimality
conditions for approximate (weakly, properly) efficient solutions of multiobjective optimization
problems. Here, tangent cone, -normal cone, cones of feasible directions, second-order tangent
set, asymptotic second-order cone, and Hadamard upper (lower) directional derivatives are used
in the characterizations. The results are first presented in convex cases and then generalized
to nonconvex cases by employing local concepts.