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A limited memory q-BFGS algorithm for unconstrained optimization problems

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Abstract

A limited memory q-BFGS (Broyden–Fletcher–Goldfarb–Shanno) method is presented for solving unconstrained optimization problems. It is derived from a modified BFGS-type update using q-derivative (quantum derivative). The use of Jackson’s derivative is an effective mechanism for escaping from local minima. The q-gradient method is complemented to generate the parameter q for computing the step length in such a way that the search process gradually shifts from global in the beginning to almost local search in the end. Further, the global convergence is established under Armijo-Wolfe conditions even if the objective function is not convex. The numerical experiments show that proposed method is potentially efficient.

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Acknowledgements

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). The fifth author was supported by Bu-Ali Sina University. The authors would also like to thank the anonymous referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. College of Economics, Shenzhen University, Shenzhen, 518060, China

    Kin Keung Lai

  2. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    Shashi Kant Mishra

  3. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India

    Geetanjali Panda

  4. Department of Mathematics, Sir Gurudas Mahavidyalaya, Kolkata, 700067, India

    Suvra Kanti Chakraborty

  5. Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan, Iran

    Mohammad Esmael Samei

  6. DST-Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    Bhagwat Ram

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  1. Kin Keung Lai
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Lai, K.K., Mishra, S.K., Panda, G. et al. A limited memory q-BFGS algorithm for unconstrained optimization problems. J. Appl. Math. Comput. 66, 183–202 (2021). https://doi.org/10.1007/s12190-020-01432-6

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