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INITIAL IMPROVEMENT OF THE HYBRID ACCELERATED GRADIENT DESCENT PROCESS

Published online by Cambridge University Press:  01 August 2018

STEFAN PANIĆ Open the ORCID record for STEFAN PANIĆ [Opens in a new window] ,
MILENA J. PETROVIĆ Open the ORCID record for MILENA J. PETROVIĆ [Opens in a new window]  and
MIROSLAVA MIHAJLOV CAREVIĆ Open the ORCID record for MIROSLAVA MIHAJLOV CAREVIĆ [Opens in a new window]
STEFAN PANIĆ
Affiliation:
Faculty of Sciences and Mathematics, University of Priština, LoleRibara 29, 29000 Kosovska Mitrovica, Serbia email stefanpnc@yahoo.com
MILENA J. PETROVIĆ*
Affiliation:
Faculty of Sciences and Mathematics, University of Priština, LoleRibara 29, 29000 Kosovska Mitrovica, Serbia email milena.petrovic@pr.ac.rs
MIROSLAVA MIHAJLOV CAREVIĆ
Affiliation:
Faculty of Mathematics and Computer Science, Alfa BK University, Palmira Toljatija 3, 11070 Belgrade, Serbia email miroslavamihajlovcarevic@yahoo.com
*
✉milena.petrovic@pr.ac.rs
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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.

Keywords

line searchgradient descent methodsNewton methodconvergence rate

MSC classification

Primary: 65K05: Mathematical programming methods
Secondary: 90C30: Nonlinear programming 90C53: Methods of quasi-Newton type
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. 

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