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A Trust Region Technique for Multiobjective Optimization Problems with Equality and Inequality Constraints

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  • Nantu Kumar Bisui

    (Indian Institute of Technology Kharagpur)

  • Geetanjali Panda

    (Indian Institute of Technology Kharagpur)

Abstract

This paper proposes a trust region algorithm for constrained multiobjective optimization problems with both equality and inequality-type constraints. At every iterating point, a subproblem is formulated using the quadratic approximation of all the objective functions and linear approximation of all the constraints. The step is evaluated using the notion of actual reduction and predicted reduction. A non-differentiable penalty function is used to handle the constraint violations. An adaptive BFGS update rule is introduced to update the matrix at every iteration. A new formula to compute the trust region radius at every iteration is provided. In addition, a spreading technique is introduced to derive a well-spread Pareto front. The global convergence of the proposed algorithm is proved under some reasonable assumptions. Furthermore, the algorithm’s superlinear rate of convergence is established. Numerical results and comparisons with existing methods are provided using a set of test problems to show the efficiency of the proposed method.

Suggested Citation

  • Nantu Kumar Bisui & Geetanjali Panda, 2025. "A Trust Region Technique for Multiobjective Optimization Problems with Equality and Inequality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 207(1), pages 1-54, October.
    • Handle: RePEc:spr:joptap:v:207:y:2025:i:1:d:10.1007_s10957-025-02756-8
    DOI: 10.1007/s10957-025-02756-8
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    References listed on IDEAS

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    1. G. Cocchi & G. Liuzzi & S. Lucidi & M. Sciandrone, 2020. "On the convergence of steepest descent methods for multiobjective optimization," Computational Optimization and Applications, Springer, vol. 77(1), pages 1-27, September.
    2. A. Mohammadi & A. L. Custódio, 2024. "A trust-region approach for computing Pareto fronts in multiobjective optimization," Computational Optimization and Applications, Springer, vol. 87(1), pages 149-179, January.
    3. V. A. Ramirez & G. N. Sottosanto, 2022. "Nonmonotone trust region algorithm for solving the unconstrained multiobjective optimization problems," Computational Optimization and Applications, Springer, vol. 81(3), pages 769-788, April.
    4. Kely D. V. Villacorta & Paulo R. Oliveira & Antoine Soubeyran, 2014. "A Trust-Region Method for Unconstrained Multiobjective Problems with Applications in Satisficing Processes," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 865-889, March.
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