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Increasing-along-rays property, vector optimization and well-posedness

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  • Ya-ping Fang
  • Nan-jing Huang

Abstract

In this paper we consider three classes of increasing-along-rays maps. We investigate the relations between increasing-along-rays property and star- shaped vector optimization. We also study well-posedness issues in star-shaped vector optimizations associated with increasing-along-rays maps. Copyright Springer-Verlag 2007

Suggested Citation

  • Ya-ping Fang & Nan-jing Huang, 2007. "Increasing-along-rays property, vector optimization and well-posedness," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(1), pages 99-114, February.
    • Handle: RePEc:spr:mathme:v:65:y:2007:i:1:p:99-114
    DOI: 10.1007/s00186-006-0113-1
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    References listed on IDEAS

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    1. B. Lemaire & C. Ould Ahmed Salem & J. P. Revalski, 2002. "Well-Posedness by Perturbations of Variational Problems," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 345-368, November.
    2. Alberto Zaffaroni, 2004. "Is every radiant function the sum of quasiconvex functions?," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(2), pages 221-233, June.
    3. T. Zolezzi, 2001. "Well-Posedness and Optimization under Perturbations," Annals of Operations Research, Springer, vol. 101(1), pages 351-361, January.
    4. M. Bianchi & N. Hadjisavvas & S. Schaible, 1997. "Vector Equilibrium Problems with Generalized Monotone Bifunctions," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 527-542, March.
    5. E. Miglierina & E. Molho & M. Rocca, 2005. "Well-Posedness and Scalarization in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 126(2), pages 391-409, August.
    6. X. X. Huang, 2001. "Pointwise Well-Posedness of Perturbed Vector Optimization Problems in a Vector-Valued Variational Principle," Journal of Optimization Theory and Applications, Springer, vol. 108(3), pages 671-684, March.
    7. E. Miglierina & E. Molho, 2003. "Well-posedness and convexity in vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(3), pages 375-385, December.
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