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    Optimal Algorithms for Affinely Constrained, Distributed, Decentralized, Minimax, and High-Order Optimization Problems

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    Thesis.pdf
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    8.042Mb
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    Description:
    PhD Dissertation
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    Type
    Dissertation
    Authors
    Kovalev, Dmitry cc
    Advisors
    Richtarik, Peter cc
    Committee members
    Nesterov, Yurii
    Nemirovski, Arkadi
    Keyes, David E. cc
    Wang, Di cc
    Parsani, Matteo cc
    Program
    Computer Science
    KAUST Department
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Date
    2022-09
    Permanent link to this record
    http://hdl.handle.net/10754/682331
    
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    Abstract
    Optimization problems are ubiquitous in all quantitative scientific disciplines, from computer science and engineering to operations research and economics. Developing algorithms for solving various optimization problems has been the focus of mathematical research for years. In the last decade, optimization research has become even more popular due to its applications in the rapidly developing field of machine learning. In this thesis, we discuss a few fundamental and well-studied optimization problem classes: decentralized distributed optimization (Chapters 2 to 4), distributed optimization under similarity (Chapter 5), affinely constrained optimization (Chapter 6), minimax optimization (Chapter 7), and high-order optimization (Chapter 8). For each problem class, we develop the first provably optimal algorithm: the complexity of such an algorithm cannot be improved for the problem class given. The proposed algorithms show state-of-the-art performance in practical applications, which makes them highly attractive for potential generalizations and extensions in the future.
    Citation
    Kovalev, D. (2022). Optimal Algorithms for Affinely Constrained, Distributed, Decentralized, Minimax, and High-Order Optimization Problems [KAUST Research Repository]. https://doi.org/10.25781/KAUST-NFIDY
    DOI
    10.25781/KAUST-NFIDY
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-NFIDY
    Scopus Count
    Collections
    PhD Dissertations; Computer Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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