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

V. V. Gorokhovik   ; M. A. Trofimovich

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 81-96

Résumé

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.

Détail

Keywords: vector optimization, nontransitive preference, nonlinear scalarization, second order optimality conditions.

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