Geodesic
First and second order optimality conditions in vector optimization problems with nontransitive preference relation
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 81-96

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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.
Keywords: vector optimization, nontransitive preference, nonlinear scalarization, second order optimality conditions. 
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     title = {First and second order optimality conditions in vector optimization problems with nontransitive preference relation},
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V. V. Gorokhovik; M. A. Trofimovich. First and second order optimality conditions in vector optimization problems with nontransitive preference relation. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 81-96. http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a7/