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Farkas-Type Results for Vector-Valued Functions with Applications

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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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Authors and Affiliations

  1. International University, Vietnam National University - HCMC, Linh Trung ward, Thu Duc district, Ho Chi Minh city, Vietnam

    N. Dinh

  2. Department of Mathematics, University of Alicante, San Vicente del Raspeig, Spain

    M. A. Goberna & M. A. López

  3. Federation University, Ballarat, Australia

    M. A. López

  4. Tien Giang University, Mỹ Tho, Tien Giang province, Vietnam

    T. H. Mo

Authors
  1. N. Dinh
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  2. M. A. Goberna
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  3. M. A. López
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  4. T. H. Mo
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Corresponding author

Correspondence to M. A. López.

Additional information

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

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