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On q-Newton’s method for unconstrained multiobjective optimization problems

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Abstract

In this paper, we present a method of so-called q-Newton’s type descent direction for solving unconstrained multiobjective optimization problems. The algorithm presented in this paper is implemented by applying an independent parameter q (quantum) in an Armijo-like rule to compute the step length which guarantees that the value of the objective function decreases at every iteration. The search processes gradually shift from global in the beginning to local as the algorithm converges due to q-gradient. The algorithm is experimented on 41 benchmark/test functions which are unimodal and multi-modal with 1, 2, 3, 4, 5, 10 and 50 different dimensions. The performance of the proposed method is confirmed by comparing with three existing schemes.

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Acknowledgements

We are grateful to the editors and anonymous referees for their valuable comments and detailed suggestions which helped to improve the quality of this paper. This research was supported by the Science and Engineering Research Board (Grant No. DST-SERB-MTR-2018/000121) and the University Grants Commission (IN) (Grant No. UGC-2015-UTT–59235).

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Authors and Affiliations

  1. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India

    Shashi Kant Mishra

  2. Department of Mathematics, Indian Institute of Technology, Kharagpur, India

    Geetanjali Panda

  3. Department of Economic Science, Indian Institute of Technology, Kanpur, India

    Md Abu Talhamainuddin Ansary

  4. DST-Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi, India

    Bhagwat Ram

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  1. Shashi Kant Mishra
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  2. Geetanjali Panda
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Correspondence to Bhagwat Ram.

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Mishra, S.K., Panda, G., Ansary, M.A.T. et al. On q-Newton’s method for unconstrained multiobjective optimization problems. J. Appl. Math. Comput. 63, 391–410 (2020). https://doi.org/10.1007/s12190-020-01322-x

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