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A subgradient supported ellipsoid method for convex multiobjective optimization problems

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  • M. Muthukani

    (Amrita Vishwa Vidyapeetham)

  • P. Paramanathan

    (Amrita Vishwa Vidyapeetham)

Abstract

Multi-objective optimization is a computational technique used to find the best solution for a problem with multiple conflicting objectives. A set of solutions that represents a trade-off between the competing objectives, known as the Pareto front or Pareto set. A common method for solving multi-objective optimization problems is the scalarization method, which converts multi objectives into a single objective. However, the scalarization may not cover the entire pareto front in complex multi-objective optimization problems. In this paper, an ellipsoid algorithm is proposed to overcome the disadvantages of the scalarization method. An ellipsoid algorithm does not combine objectives into single objective. Rather, it directly explore the solution space, aiming to find solutions that are not restricted by the limitations of scalarization. The proposed algorithm mainly targets the multi-objective optimization problems with linear constraints. Also, the convergence rate and the numerical examples justify the effectiveness of the proposed ellipsoid method.

Suggested Citation

  • M. Muthukani & P. Paramanathan, 2025. "A subgradient supported ellipsoid method for convex multiobjective optimization problems," OPSEARCH, Springer;Operational Research Society of India, vol. 62(3), pages 1239-1261, September.
    • Handle: RePEc:spr:opsear:v:62:y:2025:i:3:d:10.1007_s12597-024-00849-y
    DOI: 10.1007/s12597-024-00849-y
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    References listed on IDEAS

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    1. Michael J. Todd, 1982. "On Minimum Volume Ellipsoids Containing Part of a Given Ellipsoid," Mathematics of Operations Research, INFORMS, vol. 7(2), pages 253-261, May.
    2. Jean-Louis Goffin, 1983. "Convergence Rates of the Ellipsoid Method on General Convex Functions," Mathematics of Operations Research, INFORMS, vol. 8(1), pages 135-150, February.
    3. Vieira, D.A.G. & Lisboa, A.C., 2019. "A cutting-plane method to nonsmooth multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 275(3), pages 822-829.
    4. Frenk, J.B.G. & Gromicho, J.A.S. & Zhang, S., 1994. "A deep cut ellipsoid algorithm for convex programming," Econometric Institute Research Papers 11633, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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