Variants of the Ekeland variational principle for approximate proper solutions of vector equilibrium problems

L. P. Hai (), L. Huerga (), P. Q. Khanh () and V. Novo ()
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L. P. Hai: University of Science, Vietnam National University-Ho Chi-Minh City
L. Huerga: Universidad Nacional de Educación a Distancia
P. Q. Khanh: International University, Vietnam National University-Ho Chi Minh City
V. Novo: Universidad Nacional de Educación a Distancia

Journal of Global Optimization, 2019, vol. 74, issue 2, No 7, 382 pages

Abstract: Abstract In this paper, we provide variants of the Ekeland variational principle for a type of approximate proper solutions of a vector equilibrium problem, whose final space is finite dimensional and partially ordered by a polyhedral cone. Depending on the choice of an approximation set that defines these solutions, we prove that they approximate suitably exact weak efficient/proper efficient/efficient solutions of the problem. The variants of the Ekeland variational principle are obtained for an unconstrained and also for a cone-constrained vector equilibrium problem, through a nonlinear scalarization, and expressed by means of the matrix that defines the ordering cone, which makes them easier to handle. At the end, the results are applied to multiobjective optimization problems, for which a related vector variational inequality problem is defined.

Keywords: Ekeland variational principle; Vector equilibrium problems; Approximate proper solutions; Multiobjective optimization; Variational inequalities; 90C33; 90C26; 90C29; 49J52; 49J53 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10898-019-00772-3

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