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Robust Pareto solutions for convex quadratic multiobjective optimization problems under data uncertainty

Author

Listed:
  • T. D. Chuong

    (Deakin University)

  • V. H. Mak-Hau

    (Deakin University)

  • J. Yearwood

    (Deakin University)

  • R. Dazeley

    (Deakin University)

  • M.-T. Nguyen

    (Defence Science and Technology Group)

  • T. Cao

    (Defence Science and Technology Group)

Abstract

In this paper, we consider a convex quadratic multiobjective optimization problem, where both the objective and constraint functions involve data uncertainty. We employ a deterministic approach to examine robust optimality conditions and find robust (weak) Pareto solutions of the underlying uncertain multiobjective problem. We first present new necessary and sufficient conditions in terms of linear matrix inequalities for robust (weak) Pareto optimality of the multiobjective optimization problem. We then show that the obtained optimality conditions can be alternatively checked via other verifiable criteria including a robust Karush–Kuhn–Tucker condition. Moreover, we establish that a (scalar) relaxation problem of a robust weighted-sum optimization program of the multiobjective problem can be solved by using a semidefinite programming (SDP) problem. This provides us with a way to numerically calculate a robust (weak) Pareto solution of the uncertain multiobjective problem as an SDP problem that can be implemented using, e.g., MATLAB.

Suggested Citation

  • T. D. Chuong & V. H. Mak-Hau & J. Yearwood & R. Dazeley & M.-T. Nguyen & T. Cao, 2022. "Robust Pareto solutions for convex quadratic multiobjective optimization problems under data uncertainty," Annals of Operations Research, Springer, vol. 319(2), pages 1533-1564, December.
    • Handle: RePEc:spr:annopr:v:319:y:2022:i:2:d:10.1007_s10479-021-04461-x
    DOI: 10.1007/s10479-021-04461-x
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    References listed on IDEAS

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    1. Xiangkai Sun & Wen Tan & Kok Lay Teo, 2023. "Characterizing a Class of Robust Vector Polynomial Optimization via Sum of Squares Conditions," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 737-764, May.

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