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INITIAL IMPROVEMENT OF THE HYBRID ACCELERATED GRADIENT DESCENT PROCESS
Published online by Cambridge University Press: 01 August 2018
Abstract
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We improve the convergence properties of the iterative scheme for solving unconstrained optimisation problems introduced in Petrovic et al. [‘Hybridization of accelerated gradient descent method’, Numer. Algorithms (2017), doi:10.1007/s11075-017-0460-4] by optimising the value of the initial step length parameter in the backtracking line search procedure. We prove the validity of the algorithm and illustrate its advantages by numerical experiments and comparisons.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 98 , Issue 2 , October 2018 , pp. 331 - 338
- Copyright
- © 2018 Australian Mathematical Publishing Association Inc.
References
Andrei, N., ‘An unconstrained optimization test functions collection’, Adv. Model. Optim.
10(1) (2008), 147–161.Google Scholar
Hager, W. and Zhang, H., ‘Algorithm 851: a conjugate gradient method with guaranteed descent’, ACM Trans. Math. Software
32 (2006), 113–137.Google Scholar
Khan, S. H., ‘A Picard–Mann hybrid iterative process’, Fixed Point Theory Appl.
2013 (2013), 69.Google Scholar
Petrović, M. J., ‘An accelerated double step size method in unconstrained optimization’, Appl. Math. Comput.
250 (2015), 309–319.Google Scholar
Petrović, M., Rakocević, V., Kontrec, N., Panić, S. and Ilić, D., ‘Hybridization of accelerated gradient descent method’, Numer. Algorithms (2017), doi:10.1007/s11075-017-0460-4.Google Scholar
Petrović, M. J. and Stanimirović, P. S., ‘Accelerated double direction method for solving unconstrained optimization problems’, Math. Probl. Eng.
2014 (2014), 965104.Google Scholar
Polak, E. and Ribière, G., ‘Note sur la convergence de directions conjuguées’, Rev. Fran. Inf. Rech. Opérat.
3 (1969), 35–43.Google Scholar
Polyak, B. T., ‘The conjugate gradient method in extreme problems’, Comput. Math. Math. Phys.
9 (1969), 94–112.Google Scholar
Stanimirović, P. S. and Miladinović, M. B., ‘Accelerated gradient descent methods with line search’, Numer. Algorithms
54 (2010), 503–520.Google Scholar
Stanimirović, P. S., Milovanović, G. V. and Petrović, M. J., ‘A transformation of accelerated double step size method for unconstrained optimization’, Math. Probl. Eng.
2015 (2015), 283679.Google Scholar
Yuan, G., ‘Modified nonlinear conjugate gradient methods with sufficient descent property for large-scale optimization problems’, Optim. Lett.
3 (2009), 11–21.Google Scholar
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