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Constrained Extremum Problems and Image Space Analysis—Part II: Duality and Penalization

Author

Listed:
  • Shengjie Li

    (Chongqing University)

  • Yangdong Xu

    (Chongqing University of Posts and Telecommunications)

  • Manxue You

    (Chongqing University)

  • Shengkun Zhu

    (Southwestern University of Finance and Economics)

Abstract

In the light, as said in Part I, of showing the main feature of image space analysis—to unify and generalize the several topics of optimization—we continue, in Part II, considering duality and penalization. In the literature, they are distinct sectors of optimization and, as far as we know, they have nothing in common. Here it is shown that they can be derived by the same “root.”

Suggested Citation

  • Shengjie Li & Yangdong Xu & Manxue You & Shengkun Zhu, 2018. "Constrained Extremum Problems and Image Space Analysis—Part II: Duality and Penalization," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 637-659, June.
    • Handle: RePEc:spr:joptap:v:177:y:2018:i:3:d:10.1007_s10957-018-1248-y
    DOI: 10.1007/s10957-018-1248-y
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    References listed on IDEAS

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    1. G. Mastroeni, 2010. "Some applications of the image space analysis to the duality theory for constrained extremum problems," Journal of Global Optimization, Springer, vol. 46(4), pages 603-614, April.
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    Cited by:

    1. Kenneth O. Kortanek & Guolin Yu & Qinghong Zhang, 2021. "Strong duality for standard convex programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(3), pages 413-436, December.
    2. Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2020. "A Unified Approach Through Image Space Analysis to Robustness in Uncertain Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 466-493, February.
    3. Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2020. "Robustness Characterizations for Uncertain Optimization Problems via Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 459-479, August.
    4. Yang-Dong Xu & Cheng-Ling Zhou & Sheng-Kun Zhu, 2021. "Image Space Analysis for Set Optimization Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 311-343, October.

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