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The thesis reviews key foundations in nonlinear programming, convex and smoothness properties, subgradients and conjugate functions, along with strong convexity and non-convex non-smooth settings. It further develops and applies performance estimation problems and interpolation theorems, supported by semidefinite programming, to derive convergence-rate insights and performance bounds relevant to machine learning optimization.","Tilburg University  \nPerformance analysis of optimization methods for machine learning  \nAbbaszadehpeivasti, Hadi  \nDOI:  \n10.26116/tisem.46749783  \nPublication date:  \n2024  \nDocument Version  \nPublisher's PDF, also known as Version of record  \nLink to publication in Tilburg University Research Portal  \nCitation for published version (APA):  \nAbbaszadehpeivasti, H. (2024) . Performance analysis of optimization methods for machine learning. [Doctoral Thesis, Tilburg University] . CentER, Center for Economic Research. [https://doi.org/10.26116/tisem.46749783](https://doi.org/10.26116/tisem.46749783)  \nGeneral rights  \nCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.  \n• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.  \n• You may not further distribute the material or use it for any profit-making activity or commercial gain  \n• You may freely distribute the URL identifying the publication in the public portal  \nTake down policy  \nIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.  \nDownload date: 22. Oct. 2024  \nPerformance Analysis of Optimization Methods for Machine Learning  \nHAD I ABBAS ZA DEH PEIVASTI  \nPerformance Analysis of Optimization Methods for  \nMachine Learning  \nPROEFSCHRIFT  \nter verkrijging van de graad van doctor aan Tilburg University op gezag van de rector magnificus, prof. dr. W.B.H.J. van de Donk, in het openbaar te verdedigen ten overstaan van een door het college voor promoties aangewezen commissie in de Aula van de Universiteit op  \nvrijdag 4 oktober 2024 om 13.30 uur door  \nHadi Abbaszadehpeivasti,  \ngeboren te Tabriz, Iran  \nPROMOTORES: prof. dr. E. de Klerk (Tilburg University)  \nprof. dr. M. Laurent (Tilburg University)  \nLEDEN PROMOTIECOMMISSIE: prof. dr. I. Birbil ( University of Amsterdam)  \nprof. dr. F. Glineur (Université Catholique de Louvain) dr. M. Hochstenbach (TU Eindhoven)  \nprof. dr. J.C. Vera Lizcano (Tilburg University)  \n[prof. dr. ir. R. Sotirov](prof. dr. ir. R. Sotirov) (Tilburg University)  \nThis project was supported by the Dutch Scientific Council (NWO) Grant Optimization for and with Machine Learning (OPTIMAL), OCENW.GROOT.2019.015 .  \n©2024 Hadi Abbaszadehpeivasti, The Netherlands. All rights reserved. No parts of this thesis maybe reproduced, stored in a retrieval system or transmitted in any form or by any means without permission of the author. Alle rechten voorbehouden. Niets uit deze uitgave mag worden vermenigvuldigd, in enige vorm of op enige wijze, zonder voorafgaande schriftelijke toestemming vande auteur.  \nTo the loving souls who have enriched my life with their presence  \niv  \nAcknowledgments  \nThis thesis is a clear reflection of strong support from many people who have been vital to my academic journey. My deepest gratitude goes to my supervisor, Etienne de Klerk, and co-supervisor, Monique Laurent, for their exceptional guidance, and the wisdom they shared. Moslem Zamani, postdoctoral researcher, deserves special recognition for his invaluable assistance and insights. I would also like to express my appreciation to the members of my defense committee, Ilker Birbil, François Glineur, Michiel Hochstenbach, Juan Vera Lizcano, and Renata Sotirov, for their rigorous evaluation, which has undoubtedly improved the quality of this dissertation.  \nI would like to express my heartfelt gratitude to my mother, Batoul, for her unwavering support and inspiration throughout my academic journey. Her encouragement and belief in my abilities have been a constant source of motivation. I am deeply thankful for her boundless love and guidance, which have played a pivo","cbCais7fjAbFA4jL","https://ap.wps.com/l/cbCais7fjAbFA4jL","pdf",3838336,1,253,"English","en",105,"# Contents\n## Introduction\n## Preliminaries and interpolation theorems","[{\"question\":\"What is the main focus of this thesis?\",\"answer\":\"The thesis focuses on analyzing optimization methods used in machine learning, emphasizing theoretical performance and convergence behavior.\"},{\"question\":\"Which mathematical tools are used to support the analysis?\",\"answer\":\"It relies on foundations from nonlinear programming, convex/non-convex function properties, and interpolation theorems, with semidefinite programming used as a core technique.\"},{\"question\":\"How does the thesis connect optimization analysis with machine learning?\",\"answer\":\"It includes dedicated discussion on the relationship between machine learning and optimization and frames performance questions via performance estimation 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