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Optimality and solutions for conic robust multiobjective programs

Author

Listed:
  • Thai Doan Chuong

    (Brunel University of London, Department of Mathematics)

  • Xinghuo Yu

    (RMIT University, School of Engineering)

  • Andrew Eberhard

    (RMIT University, School of Engineering)

  • Chaojie Li

    (UNSW Sydney, School of Electrical Engineering and Telecommunications)

  • Chen Liu

    (RMIT University, School of Engineering)

Abstract

This paper presents a robust framework for handling a conic multiobjective linear optimization problem, where the objective and constraint functions are involving affinely parameterized data uncertainties. More precisely, we examine optimality conditions and calculate efficient solutions of the conic robust multiobjective linear problem. We provide necessary and sufficient linear conic criteria for efficiency of the underlying conic robust multiobjective linear program. It is shown that such optimality conditions can be expressed in terms of linear matrix inequalities and second-order conic conditions for a multiobjective semidefinite program and a multiobjective second order conic program, respectively. We show how efficient solutions of the conic robust multiobjective linear problem can be found via its conic programming reformulation problems including semidefinite programming and second-order cone programming problems. Numerical examples are also provided to illustrate that the proposed conic programming reformulation schemes can be employed to find efficient solutions for concrete problems including those arisen from practical applications.

Suggested Citation

  • Thai Doan Chuong & Xinghuo Yu & Andrew Eberhard & Chaojie Li & Chen Liu, 2025. "Optimality and solutions for conic robust multiobjective programs," Journal of Global Optimization, Springer, vol. 93(3), pages 747-776, November.
    • Handle: RePEc:spr:jglopt:v:93:y:2025:i:3:d:10.1007_s10898-025-01552-y
    DOI: 10.1007/s10898-025-01552-y
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