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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 4, Pages 81–96 (Mi timm1117)  
This article is cited in 5 scientific papers (total in 5 papers)

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

V. V. Gorokhovika, M. A. Trofimovichb

a Institute of Mathematics, National Academy of Sciences of the Republic of Belarus
b Belarusian State University
Full-text PDF (233 kB) Citations (5)
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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 the preference relation ≺ 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.
Received: 09.06.2014
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, Volume 292, Issue 1, Pages 91–105
DOI: https://doi.org/10.1134/S0081543816020085
Bibliographic databases:
Document Type: Article
UDC: 517.972.2
Language: Russian
Citation: V. V. Gorokhovik, M. A. Trofimovich, “First and second order optimality conditions in vector optimization problems with nontransitive preference relation”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 4, 2014, 81–96; Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 91–105
Citation in format AMSBIB
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\yr 2014
\vol 20
\issue 4
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  • https://www.mathnet.ru/eng/timm/v20/i4/p81
    • This publication is cited in the following 5 articles:
    1. Valentin V. Gorokhovik, “On the Extension of Quasipreferences to Weak Preferences with a Prescribed Indifference Relation”, J Math Sci, 2024  crossref
    2. A.V. Gorbunova, A.V. Lebedev, “Nontransitivity of tuples of random variables with polynomial density and its effects in Bayesian models”, Mathematics and Computers in Simulation, 202 (2022), 181  crossref
    3. V. V. Gorokhovik, “Kasatelnye vektory vysokogo poryadka k mnozhestvam i neobkhodimye usloviya minimalnosti dlya tochek uporyadochennykh podmnozhestv”, Tr. In-ta matem., 29:1-2 (2021), 52–66  mathnet
    4. A. V. Gorbunova, A. V. Lebedev, “Effekty stokhasticheskoi netranzitivnosti v sistemakh massovogo obsluzhivaniya”, UBS, 85 (2020), 23–50  mathnet  crossref
    5. A. V. Lebedev, “The nontransitivity problem for three continuous random variables”, Autom. Remote Control, 80:6 (2019), 1058–1068  mathnet  crossref  crossref  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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