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Proximal proper efficiency in set-valued optimization

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  • Ruchi, Arora
  • Lalitha, C.S.

Abstract

In this paper, we introduce the concept of cone semilocal convex and cone semilocal convexlike set-valued maps and obtain characterization of these maps in terms of locally star-shaped sets. We derive an alternative theorem involving cone semilocal convexlike set-valued maps under the assumption of closedness of the translation of the image set of the map by the cone under consideration. We introduce proximal proper efficiency for a set-valued optimization problem in finite-dimensional spaces and obtain certain scalarization and Lagrange multiplier theorems. In the end, we consider a Lagrange form of dual and establish weak and strong duality theorems.

Suggested Citation

  • Ruchi, Arora & Lalitha, C.S., 2005. "Proximal proper efficiency in set-valued optimization," Omega, Elsevier, vol. 33(5), pages 407-411, October.
    • Handle: RePEc:eee:jomega:v:33:y:2005:i:5:p:407-411
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    References listed on IDEAS

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    1. Wei Dong Rong & Yu Nan Wu, 1998. "Characterizations of super efficiency in cone-convexlike vector optimization with set-valued maps," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 247-258, November.
    2. Y. H. Cheng & W. T. Fu, 1999. "Strong efficiency in a locally convex space," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(3), pages 373-384, December.
    3. Z. F. Li, 1998. "Benson Proper Efficiency in the Vector Optimization of Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 623-649, September.
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    Cited by:

    1. Q. Q. Song & G. Q. Tang & L. S. Wang, 2013. "On Essential Stable Sets of Solutions in Set Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 591-599, March.

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