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Vector Topical Function, Abstract Convexity and Image Space Analysis

Author

Listed:
  • Chaoli Yao

    (Chongqing University)

  • Shengjie Li

    (Chongqing University)

Abstract

In this paper, we introduce a new type of vector topical function. It contains some other categories of topical functions as special cases and can be interpreted as weak separation functions in image space analysis. We establish its envelope result and investigate its properties in the frame of abstract convexity. Then, we present the corresponding conjugation and subdifferential, and observe the relationships among these concepts. Finally, as applications, we obtain some dual results for some vector optimization, where the object is expressed as the difference of vector topical functions.

Suggested Citation

  • Chaoli Yao & Shengjie Li, 2018. "Vector Topical Function, Abstract Convexity and Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 717-742, June.
    • Handle: RePEc:spr:joptap:v:177:y:2018:i:3:d:10.1007_s10957-018-1215-7
    DOI: 10.1007/s10957-018-1215-7
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    References listed on IDEAS

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    1. A. M. Rubinov & B. M. Glover, 1999. "Increasing Convex-Along-Rays Functions with Applications to Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 102(3), pages 615-642, September.
    2. A. Doagooei & H. Mohebi, 2013. "Optimization of the difference of topical functions," Journal of Global Optimization, Springer, vol. 57(4), pages 1349-1358, December.
    3. V. Jeyakumar & A. M. Rubinov & Z. Y. Wu, 2007. "Generalized Fenchel’s Conjugation Formulas and Duality for Abstract Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 132(3), pages 441-458, March.
    4. H. Mohebi, 2013. "Abstract convexity of radiant functions with applications," Journal of Global Optimization, Springer, vol. 55(3), pages 521-538, March.
    Full references (including those not matched with items on IDEAS)

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