Stochastic optimization on tensor factorization and completionStochastic optimization on tensor factorization and completion Μεταπτυχιακή Διατριβή Master Thesis 2021-03-052021enWe consider the problem of structured canonical polyadic decomposition (CPD). If the size of the problem is very big, then stochastic optimization approaches are viable alternatives to classical methods, such as Alternating Optimization (AO) and All-At-Once (AAO) optimization. We extend a recent stochastic gradient approach by employing an acceleration step (Nesterov momentum) in each iteration. We compare our approach with state-of-the-art alternatives, using both synthetic and real-world data, and find it to be very competitive. Furthermore, we examine the drawbacks of a parallel implementation of our accelerated stochastic algorithm and describe an alternative method that deals with these limitations. Finally, we propose an accelerated stochastic algorithm for the Nonnegative Tensor Completion problem and its parallel implementation via the shared–memory API OpenMP. Through numerical experiments, we test its efficiency in very large problems.http://creativecommons.org/licenses/by/4.0/Πολυτεχνείο Κρήτης::Σχολή Ηλεκτρολόγων Μηχανικών και Μηχανικών ΥπολογιστώνSiaminou_Ioanna_MSc_2021.pdfChania [Greece]Library of TUC2021-03-04application/pdf1.7 MBembargo Siaminou Ioanna Σιαμινου Ιωαννα Liavas Athanasios Λιαβας Αθανασιος Karystinos Georgios Καρυστινος Γεωργιος Samoladas Vasilis Σαμολαδας Βασιλης Πολυτεχνείο Κρήτης Technical University of Crete Tensor factorization Tensor completion Stochastic optimization Nesterov acceleration OpenMP Parallel algorithms