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Development of Global Optimization Methods by Generalized Eigenvalue Computation

Research Project

Project/Area Number 17H01699
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Mathematical informatics
Research InstitutionThe University of Tokyo

Principal Investigator

Iwata Satoru  東京大学, 大学院情報理工学系研究科, 教授 (00263161)

Co-Investigator(Kenkyū-buntansha) 武田 朗子  東京大学, 大学院情報理工学系研究科, 教授 (80361799)
中務 佑治  国立情報学研究所, 情報学プリンシプル研究系, 准教授 (10723554)
Project Period (FY) 2017-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥7,280,000 (Direct Cost: ¥5,600,000、Indirect Cost: ¥1,680,000)
Fiscal Year 2021: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2020: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords数理最適化 / 大域最適化 / 一般化固有値 / アルゴリズム / 機械学習 / 一般化固有値計算
Outline of Final Research Achievements

While non-convex optimization problems are hard to solve in general, this research has focused on those problems that have geometrical backgrounds and investigated a methodology to design efficient algorithms for obtaining globally optimal solutions. In particular, we have developed an efficient algorithm for non-convex quadratic constraint quadratic programming (QCQP) with one constraint. In addition, we exploit this algorithm to obtain relaxation solutions for general non-convex QCQP with the aid of the Lagrange multipliers.

Academic Significance and Societal Importance of the Research Achievements

これまで厳密な最適解を効率的に計算することは殆ど不可能だろうと思われていた非凸最適化問題に対して,幾何的な背景を有する特殊な問題であれば,一般化固有値計算を用いて,大域最適化を得られることを明らかにした.特に,一般の非凸無制約最適化問題の解法として広く使われている信頼領域法の中で繰り返し解く必要が生じる信頼領域部分問題(TRS)の高速解法を発表した論文は,比較的多くの研究に引用されている.その中には,3次正則化に対して手法を拡張したドイツの研究者による論文など,興味深い後続研究が現れている.

Report

(6 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • Research Products

    (34 results)

All 2022 2021 2020 2019 2018 2017 Other

All Int'l Joint Research (2 results) Journal Article (18 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 16 results,  Open Access: 3 results) Presentation (14 results) (of which Int'l Joint Research: 10 results,  Invited: 10 results)

  • [Int'l Joint Research] ブルッセル自由大学(ベルギー)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] 香港理工大学(中国)

    • Related Report
      2020 Annual Research Report
  • [Journal Article] An inexact successive quadratic approximation method for a class of difference-of-convex optimization problems2022

    • Author(s)
      Tianxiang Liu, Akiko Takeda
    • Journal Title

      Computational Optimization and Applications

      Volume: 82 Issue: 1 Pages: 141-173

    • DOI

      10.1007/s10589-022-00357-z

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Primal-dual subgradient method for constrained convex optimization problems2021

    • Author(s)
      Michael R. Metel, Akiko Takeda
    • Journal Title

      Optimization Letters

      Volume: 15 Issue: 4 Pages: 1491-1504

    • DOI

      10.1007/s11590-021-01728-x

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stochastic Proximal Methods for Non-Smooth Non-Convex Constrained Sparse Optimization2021

    • Author(s)
      Michael Metel, Akiko Takeda,
    • Journal Title

      Journal of Machine Learning Research

      Volume: 22 (115) Pages: 1-36

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Projected Gradient Method for Opinion Optimization with Limited Changes of Susceptibility to Persuasion2021

    • Author(s)
      Naoki Marumo, Atsushi Miyauchi, Akiko Takeda, Akira Tanaka
    • Journal Title

      CIKM

      Volume: 30 Pages: 1274-1283

    • DOI

      10.1145/3459637.3482408

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Gradient Method for Multilevel Optimization2021

    • Author(s)
      Ryo Sato, Mirai Tanaka, Akiko Takeda
    • Journal Title

      Advances in Neural Information Processing Systems

      Volume: 34 Pages: 7522-7533

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A weighted linear matroid parity algorithm2021

    • Author(s)
      Satoru Iwata, Yusuke Kobayashi
    • Journal Title

      SIAM Journal on Computing

      Volume: - Issue: 2 Pages: STOC17-238-STOC17-280

    • DOI

      10.1137/17m1141709

    • Related Report
      2020 Annual Research Report
  • [Journal Article] Data-driven structured noise filtering via common dynamics estimation2020

    • Author(s)
      Ivan Markovsky, Tianxiang Liu, Akiko Takeda
    • Journal Title

      IEEE Transactions on Signal Processing

      Volume: 68 Pages: 3064-3073

    • DOI

      10.1109/tsp.2020.2993676

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A hybrid penalty method for a class of optimization problems with multiple rank constraints2020

    • Author(s)
      Tianxiang Liu, Ivan Markovsky, Ting Kei Pong, Akiko Takeda
    • Journal Title

      SIAM Journal on Matrix Analysis and Applications

      Volume: 41 Issue: 3 Pages: 1260-1283

    • DOI

      10.1137/19m1269919

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Convex fairness constrained model using causal effect estimators2020

    • Author(s)
      Hikaru Ogura, Akiko Takeda
    • Journal Title

      WWW '20: Companion Proceedings of the Web Conference 2020

      Volume: - Pages: 723-732

    • DOI

      10.1145/3366424.3383556

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Robust Bayesian Model Selection for Variable Clustering with the Gaussian Graphical Model2020

    • Author(s)
      Daniel Andrade, Akiko Takeda, Kenji Fukumizu
    • Journal Title

      Statistics and Computing

      Volume: 30 Issue: 2 Pages: 351-376

    • DOI

      10.1007/s11222-019-09879-9

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Estimation of Gaussian Mixture Models via Tensor Moments with Application to Online Learning2020

    • Author(s)
      Donya Rahmani, Mahesan Niranjan, Damien Fay, Akiko Takeda, Jacek Brodzki
    • Journal Title

      Pattern Recognition Letters

      Volume: 131 Pages: 285-292

    • DOI

      10.1016/j.patrec.2020.01.001

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Finding a Stable Allocation in Polymatroid Intersection2020

    • Author(s)
      Satoru Iwata, Yu Yokoi
    • Journal Title

      Mathematics of Operations Research

      Volume: 45 Issue: 1 Pages: 63-85

    • DOI

      10.1287/moor.2018.0976

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Blossom Algorithm for Maximum Edge-Disjoint T-Paths2020

    • Author(s)
      Iwata Satoru、Yokoi Yu
    • Journal Title

      Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms

      Volume: - Pages: 1933-1944

    • DOI

      10.1137/1.9781611975994.119

    • ISBN
      9781611975994
    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Eigenvalue-based algorithm and analysis for nonconvex QCQP with one constraint2019

    • Author(s)
      Satoru Adachi, Yuji Nakatsukasa
    • Journal Title

      Mathematical Programming

      Volume: 173 Issue: 1-2 Pages: 79-116

    • DOI

      10.1007/s10107-017-1206-8

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report 2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Subspace methods for multi-channel sum-of-exponentials common dynamics estimation2019

    • Author(s)
      Ivan Markovsky,Tianxiang Liu, Akiko Takeda
    • Journal Title

      Proceedings of the 58th IEEE Conference on Decision and Control

      Volume: - Pages: 2672-2675

    • DOI

      10.1109/cdc40024.2019.9029261

    • Related Report
      2019 Annual Research Report
  • [Journal Article] Equivalences and differences in conic relaxations of combinatorial quadratic optimization problems2018

    • Author(s)
      Ito N.、Kim S.、Kojima M.、Takeda A.、Toh K.-C.
    • Journal Title

      Journal of Global Optimization

      Volume: 72 Issue: 4 Pages: 619-653

    • DOI

      10.1007/s10898-018-0676-4

    • NAID

      40021559420

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Index Reduction via Unimodular Transformations2018

    • Author(s)
      Iwata Satoru, Takamatsu Mizuyo
    • Journal Title

      SIAM Journal on Matrix Analysis and Applications

      Volume: 39 Issue: 3 Pages: 1135-1151

    • DOI

      10.1137/17m111794x

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Successive Lagrangian relaxation algorithm for nonconvex quadratic optimization2018

    • Author(s)
      Yamada Shinji、Takeda Akiko
    • Journal Title

      Journal of Global Optimization

      Volume: On-line First Issue: 2 Pages: 1-38

    • DOI

      10.1007/s10898-018-0617-2

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Presentation] Weighted Linear Matroid Parity2021

    • Author(s)
      Satoru Iwata
    • Organizer
      SIAM Conference on Optimization
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Deterministic and Stochastic Gradient Methods for Non-Smooth Non-Convex Regularized Optimization2020

    • Author(s)
      Akiko Takeda
    • Organizer
      Variational Analysis and Optimisation Webinar series
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Pfaffian and Matroid Matching2020

    • Author(s)
      Satoru Iwata
    • Organizer
      TUNGA (Theory Underlying Algorithms)
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Matroid Parity2019

    • Author(s)
      Satoru Iwata
    • Organizer
      The 12th Annual Meeting of the Asian Association for Algorithms and Computation
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Mader's Theorem on Edge-disjoint T-paths2019

    • Author(s)
      Satoru Iwata
    • Organizer
      Cargese Workshop on Combinatorial Optimization
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Group Lasso for Household Energy Consumption Prediction and Toward Nonconvex Regularizer2019

    • Author(s)
      Akiko Takeda
    • Organizer
      The PolyU AMA - RIKEN AIP Joint Workshop on Optimization and Machine Learning
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Efficient DC algorithm for nonconvex sparse optimization problems2019

    • Author(s)
      kiko Takeda, Jun-ya Gotoh, Katsuya Tono
    • Organizer
      International Conference on Optimization: Techniques and Applications
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Nonconvex Quadratic Optimization with One or Two Constraints2019

    • Author(s)
      Akiko Takeda
    • Organizer
      National Taiwan Normal University
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Hyperparameter Learning via Bilevel Nonsmooth Optimization2018

    • Author(s)
      Akiko Takeda
    • Organizer
      The Workshop on Variational Analysis and Stochastic Optimization
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On the roles of eigenvalues in optimization2018

    • Author(s)
      Yuji Nakatsukasa
    • Organizer
      3rd International Symposium on Research and Education of Computational Science
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Index Reduction via Unimodular Transformation2018

    • Author(s)
      Satoru Iwata
    • Organizer
      International Symposium on Mathematical Programmig
    • Related Report
      2018 Annual Research Report
  • [Presentation] Global optimization via eigenvalues2018

    • Author(s)
      Yuji Nakatsukasa
    • Organizer
      Theory and Algorithms in Data Science Seminar, Alan Turing Institute (UK)
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Global optimization via eigenvalues2017

    • Author(s)
      Yuji Nakatsukasa
    • Organizer
      Householder Symposium
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Nonconvex Quadratic Optimization with One or Two Constraints2017

    • Author(s)
      Akiko Takeda
    • Organizer
      Colloquium at Department of Applied Mathematics, The Hong Kong Polytechnic University
    • Related Report
      2017 Annual Research Report
    • Invited

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Published: 2017-04-28   Modified: 2023-01-30  

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