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 ≺-minimizers of vector-valued mappings over feasible sets with respect to a nontransitive preference relation ≺. Using an analytical representation of a preference relation ≺ in terms of a suitable family of sublinear functions, we reduce the vector optimization problem under study to a scalar inequality, from which, using the tools of variational analysis, we derive minimality conditions for the initial vector optimization problem.