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First and Second-Order Optimality Conditions for Convex Composite Multiobjective Optimization

Author

Listed:
  • X. Q. Yang

    (University of Western Australia)

  • V. Jeyakumar

    (University of New South Wales)

Abstract

Multiobjective optimization is a useful mathematical model in order to investigate real-world problems with conflicting objectives, arising from economics, engineering, and human decision making. In this paper, a convex composite multiobjective optimization problem, subject to a closed convex constraint set, is studied. New first-order optimality conditions for a weakly efficient solution of the convex composite multiobjective optimization problem are established via scalarization. These conditions are then extended to derive second-order optimality conditions.

Suggested Citation

  • X. Q. Yang & V. Jeyakumar, 1997. "First and Second-Order Optimality Conditions for Convex Composite Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 209-224, October.
    • Handle: RePEc:spr:joptap:v:95:y:1997:i:1:d:10.1023_a:1022695714596
    DOI: 10.1023/A:1022695714596
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    Cited by:

    1. Xi Yin Zheng & Runxin Li, 2014. "Lagrange Multiplier Rules for Weak Approximate Pareto Solutions of Constrained Vector Optimization Problems in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 665-679, August.
    2. X.X. Huang & X.Q. Yang, 2003. "Convergence Analysis of a Class of Nonlinear Penalization Methods for Constrained Optimization via First-Order Necessary Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 116(2), pages 311-332, February.

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