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Intersection Theorems with Applications in Optimization

Author

Listed:
  • Ravi P. Agarwal

    (Texas A&M University-Kingsville
    Florida Institute of Technology)

  • Mircea Balaj

    (University of Oradea)

  • Donal O’Regan

    (National University of Ireland)

Abstract

In this paper, we establish two intersection theorems which are useful in considering some optimization problems (complementarity problems, variational inequalities, minimax inequalities, saddle point problems).

Suggested Citation

  • Ravi P. Agarwal & Mircea Balaj & Donal O’Regan, 2018. "Intersection Theorems with Applications in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 761-777, December.
    • Handle: RePEc:spr:joptap:v:179:y:2018:i:3:d:10.1007_s10957-018-1331-4
    DOI: 10.1007/s10957-018-1331-4
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    References listed on IDEAS

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    1. Junyi Fu & Sanhua Wang, 2013. "Generalized strong vector quasi-equilibrium problem with domination structure," Journal of Global Optimization, Springer, vol. 55(4), pages 839-847, April.
    2. Ravi P. Agarwal & Mircea Balaj & Donal O’Regan, 2017. "Common Fixed Point Theorems in Topological Vector Spaces via Intersection Theorems," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 443-458, May.
    3. Suhel Khan, 2011. "Generalized vector implicit quasi complementarity problems," Journal of Global Optimization, Springer, vol. 49(4), pages 695-705, April.
    4. G. Isac & V. V. Kalashnikov, 2001. "Exceptional Family of Elements, Leray–Schauder Alternative, Pseudomonotone Operators and Complementarity," Journal of Optimization Theory and Applications, Springer, vol. 109(1), pages 69-83, April.
    5. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, October.
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    Cited by:

    1. Raúl Fierro, 2021. "An Intersection Theorem for Topological Vector Spaces and Applications," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 118-133, October.
    2. Mircea Balaj & Dan Florin Serac, 2023. "Generalized Equilibrium Problems," Mathematics, MDPI, vol. 11(9), pages 1-11, May.
    3. Mircea Balaj, 2021. "Intersection theorems for generalized weak KKM set‐valued mappings with applications in optimization," Mathematische Nachrichten, Wiley Blackwell, vol. 294(7), pages 1262-1276, July.

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