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Solving Two-stage Quadratic Multiobjective Problems via Optimality and Relaxations

Author

Listed:
  • Thai Doan Chuong

    (Brunel University London)

  • Xinghuo Yu

    (RMIT University)

  • Chen Liu

    (RMIT University)

  • Andrew Eberhard

    (RMIT University)

  • Chaojie Li

    (UNSW Sydney)

Abstract

This paper focuses on the study of robust two-stage quadratic multiobjective optimization problems. We formulate new necessary and sufficient optimality conditions for a robust two-stage multiobjective optimization problem. The obtained optimality conditions are presented by means of linear matrix inequalities and thus they can be numerically validated by using a semidefinite programming problem. The proposed optimality conditions can be elaborated further as second-order conic expressions for robust two-stage quadratic multiobjective optimization problems with separable functions and ellipsoidal uncertainty sets. We also propose relaxation schemes for finding a (weak) efficient solution of the robust two-stage multiobjective problem by employing associated semidefinite programming or second-order cone programming relaxations. Moreover, numerical examples are given to demonstrate the solution variety of our flexible models and the numerical verifiability of the proposed schemes.

Suggested Citation

  • Thai Doan Chuong & Xinghuo Yu & Chen Liu & Andrew Eberhard & Chaojie Li, 2024. "Solving Two-stage Quadratic Multiobjective Problems via Optimality and Relaxations," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 676-713, October.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:1:d:10.1007_s10957-024-02528-w
    DOI: 10.1007/s10957-024-02528-w
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    References listed on IDEAS

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