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

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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.

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Acknowledgements

The authors are grateful to a referee for the valuable comments and suggestions. This research is funded by Vietnam National University Ho Chi Minh City (VNU-HCM) under grant number T2024-26-01.

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Authors and Affiliations

  1. Vietnam National University, Ho Chi Minh City, Vietnam

    Cao Thanh Tinh

  2. Department of Mathematics and Physics, University of Information Technology, Ho Chi Minh City, Vietnam

    Cao Thanh Tinh

  3. Department of Mathematics, Brunel University London, London, United Kingdom

    Thai Doan Chuong

  4. Department of Mathematics and Applications, Saigon University, 273 An Duong Vuong Street, District 5, Ho Chi Minh City, Vietnam

    Thai Doan Chuong

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  1. Cao Thanh Tinh
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Correspondence to Cao Thanh Tinh.

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Tinh, C.T., Chuong, T.D. Robust second order cone conditions and duality for multiobjective problems under uncertainty data. J Glob Optim 88, 901–926 (2024). https://doi.org/10.1007/s10898-023-01335-3

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  • DOI: https://doi.org/10.1007/s10898-023-01335-3

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