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

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Abstract

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.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Belarus, ul. Surganova 11, Minsk, 220072, Belarus

    V. V. Gorokhovik

  2. Belarusian State University, pr. Nezavisimosti 4, Minsk, 220030, Belarus

    M. A. Trafimovich

Authors
  1. V. V. Gorokhovik
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  2. M. A. Trafimovich
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Correspondence to V. V. Gorokhovik.

Additional information

Original Russian Text © V.V. Gorokhovik, M.A.Trafimovich, 2014, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Vol. 20, No. 4.

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Gorokhovik, V.V., Trafimovich, M.A. First and second order optimality conditions in vector optimization problems with nontransitive preference relation. Proc. Steklov Inst. Math. 292 (Suppl 1), 91–105 (2016). https://doi.org/10.1134/S0081543816020085

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