Numer Algor https://doi.org/10.1007/s11075-017-0460-4 ORIGINAL PAPER Hybridization of accelerated gradient descent method Milena Petrovi´ c 1 · Vladimir Rakoˇ cevi´ c 2,3 · Nataˇ sa Kontrec 1 · Stefan Pani´ c 1 · Dejan Ili´ c 3 Received: 7 December 2016 / Accepted: 11 December 2017 © Springer Science+Business Media, LLC, part of Springer Nature 2017 Abstract We present a gradient descent algorithm with a line search procedure for solving unconstrained optimization problems which is defined as a result of applying Picard-Mann hybrid iterative process on accelerated gradient descent SM method described in Stanimirovi´ c and Miladinovi´ c (Numer. Algor. 54, 503–520, 2010). Using merged features of both analyzed models, we show that new accelerated gradi- ent descent model converges linearly and faster then the starting SM method which is confirmed trough displayed numerical test results. Three main properties are tested: number of iterations, CPU time and number of function evaluations. The efficiency of the proposed iteration is examined for the several values of the correction parameter introduced in Khan (2013).  Milena Petrovi´ c milena.petrovic@pr.ac.rs Vladimir Rakoˇ cevi´ c vrakoc@sbb.rs Nataˇ sa Kontrec natasa.kontrec@pr.ac.rs Stefan Pani´ c stefanpnc@yahoo.com Dejan Ili´ c ilicde@ptt.rs 1 Faculty of Sciences and Mathematics, University of Priˇ stina, Lole Ribara 29, 29000 Kosovska Mitrovica, Serbia 2 Serbian Academy of Sciences and Arts, Kneza Mihaila 35, 11000 Belgrade, Serbia 3 Faculty of Sciences and Mathematics, University of Niˇ s, Viˇ segradska 33, 18000 Niˇ s, Serbia