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Generalized Fenchel’s Conjugation Formulas and Duality for Abstract Convex Functions

Author

Listed:
  • V. Jeyakumar

    (University of New South Wales)

  • A. M. Rubinov

    (University of Ballarat)

  • Z. Y. Wu

    (Chongqing Normal University)

Abstract

In this paper, we present a generalization of Fenchel’s conjugation and derive infimal convolution formulas, duality and subdifferential (and ε-subdifferential) sum formulas for abstract convex functions. The class of abstract convex functions covers very broad classes of nonconvex functions. A nonaffine global support function technique and an extended sum-epiconjugate technique of convex functions play a crucial role in deriving the results for abstract convex functions. An additivity condition involving global support sets serves as a constraint qualification for the duality.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:132:y:2007:i:3:d:10.1007_s10957-007-9185-1
    DOI: 10.1007/s10957-007-9185-1
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    Citations

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    Cited by:

    1. Satoshi Suzuki & Daishi Kuroiwa, 2012. "Necessary and Sufficient Constraint Qualification for Surrogate Duality," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 366-377, February.
    2. 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.
    3. Amar Andjouh & Mohand Ouamer Bibi, 2022. "Adaptive Global Algorithm for Solving Box-Constrained Non-convex Quadratic Minimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 360-378, January.
    4. Z. Y. Wu & A. M. Rubinov, 2010. "Global Optimality Conditions for Some Classes of Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 164-185, April.
    5. Elimhan N. Mahmudov, 2020. "Infimal Convolution and Duality in Problems with Third-Order Discrete and Differential Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 781-809, March.
    6. H. Mohebi & J.-E. Martínez-Legaz & M. Rocco, 2012. "Some criteria for maximal abstract monotonicity," Journal of Global Optimization, Springer, vol. 53(2), pages 137-163, June.

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