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Duality and Exact Penalization for Vector Optimization via Augmented Lagrangian

Author

Listed:
  • X. X. Huang

    (Chongqing Normal University)

  • X. Q. Yang

    (Hong Kong Polytechnic University)

Abstract

In this paper, we introduce an augmented Lagrangian function for a multiobjective optimization problem with an extended vector-valued function. On the basis of this augmented Lagrangian, set-valued dual maps and dual optimization problems are constructed. Weak and strong duality results are obtained. Necessary and sufficient conditions for uniformly exact penalization and exact penalization are established. Finally, comparisons of saddle-point properties are made between a class of augmented Lagrangian functions and nonlinear Lagrangian functions for a constrained multiobjective optimization problem.

Suggested Citation

  • X. X. Huang & X. Q. Yang, 2001. "Duality and Exact Penalization for Vector Optimization via Augmented Lagrangian," Journal of Optimization Theory and Applications, Springer, vol. 111(3), pages 615-640, December.
    • Handle: RePEc:spr:joptap:v:111:y:2001:i:3:d:10.1023_a:1012654128753
    DOI: 10.1023/A:1012654128753
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    Cited by:

    1. Xinsheng Xu & Zhiqing Meng & Jianwu Sun & Liguo Huang & Rui Shen, 2013. "A second-order smooth penalty function algorithm for constrained optimization problems," Computational Optimization and Applications, Springer, vol. 55(1), pages 155-172, May.
    2. A. Y. Azimov, 2008. "Duality for Set-Valued Multiobjective Optimization Problems, Part 1: Mathematical Programming," Journal of Optimization Theory and Applications, Springer, vol. 137(1), pages 61-74, April.
    3. X. X. Huang & X. Q. Yang, 2004. "Duality for Multiobjective Optimization via Nonlinear Lagrangian Functions," Journal of Optimization Theory and Applications, Springer, vol. 120(1), pages 111-127, January.
    4. X. X. Huang & X. Q. Yang, 2003. "A Unified Augmented Lagrangian Approach to Duality and Exact Penalization," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 533-552, August.

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