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Optimization Problems with Cone Constraints in Groups and Semigroups: An Approach Based on Image Space Analysis

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  • Jun Li

    (China West Normal University)

  • Giandomenico Mastroeni

    (University of Pisa)

Abstract

In this paper, a class of optimization problems with cone constraints in groups and semigroups is investigated by exploiting the image space analysis. Optimality is proved by means of separation arguments in the image space associated with the given problem, which turns out to be equivalent to the existence of saddle points of generalized Lagrangian functions under suitable assumptions. In particular, Lagrangian-type sufficient or necessary optimality conditions are obtained by introducing convex-like functions and using separation theorems between convex sets in groups and semigroups obtained by Li and Mastroeni.

Suggested Citation

  • Jun Li & Giandomenico Mastroeni, 2023. "Optimization Problems with Cone Constraints in Groups and Semigroups: An Approach Based on Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 973-1007, March.
    • Handle: RePEc:spr:joptap:v:196:y:2023:i:3:d:10.1007_s10957-023-02161-z
    DOI: 10.1007/s10957-023-02161-z
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    References listed on IDEAS

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    1. Kazuo Murota & Akiyoshi Shioura, 1999. "M-Convex Function on Generalized Polymatroid," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 95-105, February.
    2. 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.
    3. 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.
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