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Robust second order cone conditions and duality for multiobjective problems under uncertainty data

Author

Listed:
  • Cao Thanh Tinh

    (Vietnam National University
    University of Information Technology)

  • Thai Doan Chuong

    (Brunel University London
    Saigon University)

Abstract

This paper studies a class of multiobjective convex polynomial problems, where both the constraint and objective functions involve uncertain parameters that reside in ellipsoidal uncertainty sets. Employing the robust deterministic approach, we provide necessary conditions and sufficient conditions, which are exhibited in relation to second order cone conditions, for robust (weak) Pareto solutions of the uncertain multiobjective optimization problem. A dual multiobjective problem is proposed to examine robust converse, robust weak and robust strong duality relations between the primal and dual problems. Moreover, we establish robust solution relationships between the uncertain multiobjective optimization program and a (scalar) second order cone programming relaxation problem of a corresponding weighted-sum optimization problem. This in particular shows that we can find a robust (weak) Pareto solution of the uncertain multiobjective optimization problem by solving a second order cone programming relaxation.

Suggested Citation

  • Cao Thanh Tinh & Thai Doan Chuong, 2024. "Robust second order cone conditions and duality for multiobjective problems under uncertainty data," Journal of Global Optimization, Springer, vol. 88(4), pages 901-926, April.
    • Handle: RePEc:spr:jglopt:v:88:y:2024:i:4:d:10.1007_s10898-023-01335-3
    DOI: 10.1007/s10898-023-01335-3
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    References listed on IDEAS

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    1. Davide La Torre & Franklin Mendivil, 2018. "Stochastic linear optimization under partial uncertainty and incomplete information using the notion of probability multimeasure," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 69(10), pages 1549-1556, October.
    2. Thai Doan Chuong, 2022. "Second-order cone programming relaxations for a class of multiobjective convex polynomial problems," Annals of Operations Research, Springer, vol. 311(2), pages 1017-1033, April.
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    4. T. D. Chuong & V. Jeyakumar & G. Li, 2019. "A new bounded degree hierarchy with SOCP relaxations for global polynomial optimization and conic convex semi-algebraic programs," Journal of Global Optimization, Springer, vol. 75(4), pages 885-919, December.
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