First and second order optimality conditions in vector optimization problems with nontransitive preference relation

We present first and second order conditions, both necessary and sufficient, for $\prec$-minimizers of vector-valued mappings over feasible sets with respect to a nontransitive preference relation $\prec$. Using an analytical representation of the preference relation $\prec$ by means of a suitable family of sublinear functions, we reduce the vector optimization problem under study to a scalar inequality, from which with the tools of variational analysis we then derive minimality conditions for the initial vector optimization problem.