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Order-Preserving Transformations and Applications

Author

Listed:
  • A. Cambini

    (University of Pisa)

  • D.T. Luc

    (University of Avignon
    Institute of Mathematics)

  • L. Martein

    (University of Pisa)

Abstract

In this paper, we study the effects of a linear transformation on the partial order relations that are generated by a closed and convex cone in a finite-dimensional space. Sufficient conditions are provided for a transformation preserving a given order. They are applied to derive the relationship between the efficient set of a set and its image under a linear transformation, to characterize generalized convex vector functions by using order-preserving transformations, to establish some calculus rules for the subdifferential of a convex vector function, and develop an optimality condition for a convex vector problem.

Suggested Citation

  • A. Cambini & D.T. Luc & L. Martein, 2003. "Order-Preserving Transformations and Applications," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 275-293, August.
    • Handle: RePEc:spr:joptap:v:118:y:2003:i:2:d:10.1023_a:1025495204834
    DOI: 10.1023/A:1025495204834
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    References listed on IDEAS

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    1. The Luc, Dinh, 1995. "On the properly efficient points of nonconvex sets," European Journal of Operational Research, Elsevier, vol. 86(2), pages 332-336, October.
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    Cited by:

    1. Elena Molho & Domenico Scopelliti, 2023. "On the study of multistage stochastic vector quasi-variational problems," Journal of Global Optimization, Springer, vol. 86(4), pages 931-952, August.
    2. Ovidiu Bagdasar & Nicolae Popovici, 2018. "Unifying local–global type properties in vector optimization," Journal of Global Optimization, Springer, vol. 72(2), pages 155-179, October.
    3. A. Engau & M. M. Wiecek, 2007. "Cone Characterizations of Approximate Solutions in Real Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 499-513, September.

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