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On q -Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems

Author

Listed:
  • Kin Keung Lai

    (College of Economics, Shenzhen University, Shenzhen 518060, China
    These authors contributed equally to this work.)

  • Shashi Kant Mishra

    (Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India
    These authors contributed equally to this work.)

  • Bhagwat Ram

    (DST-Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi 221005, India
    These authors contributed equally to this work.)

Abstract

A parameter-free optimization technique is applied in Quasi-Newton’s method for solving unconstrained multiobjective optimization problems. The components of the Hessian matrix are constructed using q -derivative, which is positive definite at every iteration. The step-length is computed by an Armijo-like rule which is responsible to escape the point from local minimum to global minimum at every iteration due to q -derivative. Further, the rate of convergence is proved as a superlinear in a local neighborhood of a minimum point based on q -derivative. Finally, the numerical experiments show better performance.

Suggested Citation

  • Kin Keung Lai & Shashi Kant Mishra & Bhagwat Ram, 2020. "On q -Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems," Mathematics, MDPI, vol. 8(4), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:616-:d:346816
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    References listed on IDEAS

    as
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    6. Saul Gass & Thomas Saaty, 1955. "The computational algorithm for the parametric objective function," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 39-45, March.
    7. Gouvêa, Érica J.C. & Regis, Rommel G. & Soterroni, Aline C. & Scarabello, Marluce C. & Ramos, Fernando M., 2016. "Global optimization using q-gradients," European Journal of Operational Research, Elsevier, vol. 251(3), pages 727-738.
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    Cited by:

    1. L. F. Prudente & D. R. Souza, 2022. "A Quasi-Newton Method with Wolfe Line Searches for Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 1107-1140, September.
    2. Kin Keung Lai & Shashi Kant Mishra & Ravina Sharma & Manjari Sharma & Bhagwat Ram, 2023. "A Modified q-BFGS Algorithm for Unconstrained Optimization," Mathematics, MDPI, vol. 11(6), pages 1-24, March.
    3. Kin Keung Lai & Shashi Kant Mishra & Bhagwat Ram & Ravina Sharma, 2023. "A Conjugate Gradient Method: Quantum Spectral Polak–Ribiére–Polyak Approach for Unconstrained Optimization Problems," Mathematics, MDPI, vol. 11(23), pages 1-14, December.

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