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Generalized $${\varepsilon }$$ ε -quasi solutions of set optimization problems

Author

Listed:
  • C. Gutiérrez

    (University of Valladolid)

  • R. López

    (Universidad de Tarapacá)

  • J. Martínez

    (Universidad de Tarapacá)

Abstract

We introduce notions of generalized $$\varepsilon $$ ε -quasi solutions to approximate set type solutions of set optimization problems. We study their properties, consistency and limit behavior as approximations to efficient and strict weak efficient solutions. Moreover, we prove an existence result for such solutions and a bound for their asymptotic cone. Finally, we obtain optimality conditions for them.

Suggested Citation

  • C. Gutiérrez & R. López & J. Martínez, 2022. "Generalized $${\varepsilon }$$ ε -quasi solutions of set optimization problems," Journal of Global Optimization, Springer, vol. 82(3), pages 559-576, March.
    • Handle: RePEc:spr:jglopt:v:82:y:2022:i:3:d:10.1007_s10898-021-01098-9
    DOI: 10.1007/s10898-021-01098-9
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    References listed on IDEAS

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    1. Y. Gao & S. H. Hou & X. M. Yang, 2012. "Existence and Optimality Conditions for Approximate Solutions to Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 152(1), pages 97-120, January.
    2. J. Dutta, 2005. "Necessary optimality conditions and saddle points for approximate optimization in banach spaces," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 127-143, June.
    3. C. Gutiérrez & B. Jiménez & V. Novo, 2015. "Optimality Conditions for Quasi-Solutions of Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 796-820, December.
    4. Qiusheng Qiu & Xinmin Yang, 2010. "Some properties of approximate solutions for vector optimization problem with set-valued functions," Journal of Global Optimization, Springer, vol. 47(1), pages 1-12, May.
    5. C. Gutiérrez & B. Jiménez & V. Novo, 2011. "A generic approach to approximate efficiency and applications to vector optimization with set-valued maps," Journal of Global Optimization, Springer, vol. 49(2), pages 313-342, February.
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