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Image Space Analysis and Scalarization of Multivalued Optimization

Author

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  • M. Chinaie

    (University of Isfahan)

  • J. Zafarani

    (Sheikhbahaee University and University of Isfahan)

Abstract

Using a new method based on generalized sections of feasible sets, we obtain optimality conditions for vector optimization of objective multifunctions with multivalued constraints.

Suggested Citation

  • M. Chinaie & J. Zafarani, 2009. "Image Space Analysis and Scalarization of Multivalued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 451-467, September.
    • Handle: RePEc:spr:joptap:v:142:y:2009:i:3:d:10.1007_s10957-009-9531-6
    DOI: 10.1007/s10957-009-9531-6
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    References listed on IDEAS

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    1. Joël Benoist & Nicolae Popovici, 2003. "Characterizations of convex and quasiconvex set-valued maps," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(3), pages 427-435, August.
    2. 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.
    3. X. Q. Yang, 1998. "Directional derivatives for set-valued mappings and applications," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 273-285, November.
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    Citations

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    Cited by:

    1. Zhiang Zhou & Wang Chen & Xinmin Yang, 2019. "Scalarizations and Optimality of Constrained Set-Valued Optimization Using Improvement Sets and Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 944-962, December.
    2. Luis Rodríguez-Marín & Miguel Sama, 2013. "Scalar Lagrange Multiplier Rules for Set-Valued Problems in Infinite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 683-700, March.
    3. Johannes Jahn & Truong Xuan Duc Ha, 2011. "New Order Relations in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 209-236, February.
    4. Hezhi Luo & Huixian Wu & Jianzhen Liu, 2015. "On Saddle Points in Semidefinite Optimization via Separation Scheme," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 113-150, April.
    5. Takashi Maeda, 2012. "On Optimization Problems with Set-Valued Objective Maps: Existence and Optimality," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 263-279, May.
    6. Jiawei Chen & Shengjie Li & Zhongping Wan & Jen-Chih Yao, 2015. "Vector Variational-Like Inequalities with Constraints: Separation and Alternative," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 460-479, August.
    7. J. Li & N. J. Huang, 2010. "Image Space Analysis for Vector Variational Inequalities with Matrix Inequality Constraints and Applications," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 459-477, June.
    8. Liu He & Qi-Lin Wang & Ching-Feng Wen & Xiao-Yan Zhang & Xiao-Bing Li, 2019. "A Kind of New Higher-Order Mond-Weir Type Duality for Set-Valued Optimization Problems," Mathematics, MDPI, vol. 7(4), pages 1-18, April.
    9. S. J. Li & Y. D. Xu & S. K. Zhu, 2012. "Nonlinear Separation Approach to Constrained Extremum Problems," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 842-856, September.
    10. M. Chinaie & J. Zafarani, 2013. "Image Space Analysis and Scalarization for ε-Optimization of Multifunctions," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 685-695, June.
    11. Y. D. Xu & S. J. Li, 2013. "Optimality Conditions for Generalized Ky Fan Quasi-Inequalities with Applications," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 663-684, June.
    12. 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.
    13. J. Li & S. Q. Feng & Z. Zhang, 2013. "A Unified Approach for Constrained Extremum Problems: Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 69-92, October.
    14. A. Moldovan & L. Pellegrini, 2009. "On Regularity for Constrained Extremum Problems. Part 2: Necessary Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 165-183, July.

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