Abstract
The main purpose of this paper consists of providing characterizations of the inclusion of the solution set of a given conic system posed in a real locally convex topological space into a variety of subsets of the same space defined by means of vector-valued functions. These Farkas-type results are used to derive characterizations of the weak solutions of vector optimization problems (including multiobjective and scalar ones), vector variational inequalities, and vector equilibrium problems.
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Acknowledgements
This research was partially supported by MINECO of Spain and FEDER of EU, Grant MTM2014-59179-C2-1-P, by the project DP160100854 from the Australian Research Council, and by the project B2015-28-04: “A new approach to some classes of optimization problems” from the Vietnam National University - HCM city, Vietnam. The authors are grateful to Dang Hai Long, of Tien Giang University, for having suggested Lemma 2.1.
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Communicated by Nicolas Hadjisavvas.
This paper is devoted to the memory of Prof. Vladimir F. Demyanov.
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Dinh, N., Goberna, M.A., López, M.A. et al. Farkas-Type Results for Vector-Valued Functions with Applications. J Optim Theory Appl 173, 357–390 (2017). https://doi.org/10.1007/s10957-016-1055-2
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DOI: https://doi.org/10.1007/s10957-016-1055-2