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    Complexity iteration analysis for strongly convex multi-objective optimization using a Newton path-following procedure

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    convexcomplexity.pdf
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    Description:
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    Type
    Article
    Authors
    Bergou, El Houcine
    Diouane, Youssef
    Kungurtsev, Vyacheslav
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2020-07-23
    Online Publication Date
    2020-07-23
    Print Publication Date
    2021-06
    Embargo End Date
    2021-07-23
    Submitted Date
    2020-03-07
    Permanent link to this record
    http://hdl.handle.net/10754/664521
    
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    Abstract
    In this note, we consider the iteration complexity of solving strongly convex multi-objective optimization problems. We discuss the precise meaning of this problem, noting that its definition is ambiguous, and focus on the most natural notion of finding a set of Pareto optimal points across a grid of scalarized problems. We prove that, in most cases, performing sensitivity based path-following after obtaining one solution is the optimal strategy for this task in terms of iteration complexity.
    Citation
    Bergou, E.-H., Diouane, Y., & Kungurtsev, V. (2020). Complexity iteration analysis for strongly convex multi-objective optimization using a Newton path-following procedure. Optimization Letters. doi:10.1007/s11590-020-01623-x
    Sponsors
    We would like to thank two anonymous referees for their careful readings and corrections that helped us to improve our manuscript significantly. E. Bergou received support from the AgreenSkills+ fellowship programme which has received funding from the EU’s Seventh Framework Programme under Grant Agreement No. FP7-609398 (AgreenSkills+ contract). V. Kungurtsev received support from the OP VVV Project CZ.02.1.01/0.0/0.0/16_019/0000765 “Research Center for Informatics”.
    Publisher
    Springer Nature
    Journal
    Optimization Letters
    DOI
    10.1007/s11590-020-01623-x
    arXiv
    2004.02979
    Additional Links
    http://link.springer.com/10.1007/s11590-020-01623-x
    ae974a485f413a2113503eed53cd6c53
    10.1007/s11590-020-01623-x
    Scopus Count
    Collections
    Articles; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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