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Separation Theorem Based on the Quasirelative Interior and Application to Duality Theory

Author

Listed:
  • F. Cammaroto

    (University of Messina)

  • B. Di Bella

    (University of Messina)

Abstract

We present a separation theorem in which the classic interior is replaced by the quasirelative interior. We apply this result to a constrained problem in the infinite-dimensional convex case, making use of a condition replacing the standard Slater condition, which in some cases can fail.

Suggested Citation

  • F. Cammaroto & B. Di Bella, 2005. "Separation Theorem Based on the Quasirelative Interior and Application to Duality Theory," Journal of Optimization Theory and Applications, Springer, vol. 125(1), pages 223-229, April.
    • Handle: RePEc:spr:joptap:v:125:y:2005:i:1:d:10.1007_s10957-004-1724-4
    DOI: 10.1007/s10957-004-1724-4
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    Cited by:

    1. Adela Capătă, 2012. "Optimality Conditions for Extended Ky Fan Inequality with Cone and Affine Constraints and Their Applications," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 661-674, March.
    2. R. I. Boţ & E. R. Csetnek & A. Moldovan, 2008. "Revisiting Some Duality Theorems via the Quasirelative Interior in Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 67-84, October.
    3. J. Li & G. Mastroeni, 2016. "Image Convexity of Generalized Systems with Infinite-Dimensional Image and Applications," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 91-115, April.
    4. Fabián Flores-Bazán & Giandomenico Mastroeni & Cristián Vera, 2019. "Proper or Weak Efficiency via Saddle Point Conditions in Cone-Constrained Nonconvex Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 787-816, June.
    5. Z. A. Zhou & X. M. Yang, 2011. "Optimality Conditions of Generalized Subconvexlike Set-Valued Optimization Problems Based on the Quasi-Relative Interior," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 327-340, August.
    6. J. Li & L. Yang, 2018. "Set-Valued Systems with Infinite-Dimensional Image and Applications," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 868-895, December.
    7. Do Luu & Dinh Hang, 2014. "Efficient solutions and optimality conditions for vector equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(2), pages 163-177, April.

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