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2022 年度 実施状況報告書

錐最適化における悪条件問題の求解

研究課題

研究課題/領域番号 19K20217
研究機関統計数理研究所

研究代表者

ロウレンソ ブルノ・フィゲラ  統計数理研究所, 数理・推論研究系, 准教授 (80778720)

研究期間 (年度) 2019-04-01 – 2024-03-31
キーワードerror bounds / amenable cones / facial residual function / hyperbolicity cones / self-duality / automorphism group
研究実績の概要

(a) We completed several preprints on the following topics: geometry of hyperbolicity cones, error bounds for power cones and self-duality of polyhedral cones. Among our results, we were able to show that all hyperbolicity cones are amenable and we also investigated their automorphism group under certain conditions. For power cones, we completely determined their error bounds and automorphisms. Finally, we showed that self-duality for a polyhedral cone can be completely detected through the positive semidefiniteness of one of its slack matrices and we showed a surprising connection between slack matrices of irreducible self-dual polyhedral cones and extreme rays of doubly nonnegative matrices.
(b) Following the revision of papers that were in peer-review in the previous fiscal year, several of those papers were finally accepted at important journals in optimization and neighbouring areas. This includes papers in SIAM Journal on Optimization, SIAM Journal on Applied Algebra and Geometry, SIAM Journal on Matrix Analysis, Mathematical Programming and Foundations of Computational Mathematics.
(c) We presented our results in workshops and conferences both online and in-person. There were also research visits to collaborators in Australia and Brazil.

現在までの達成度 (区分)
現在までの達成度 (区分)

2: おおむね順調に進展している

理由

Several preprints were completed and several papers were accepted at important journals in optimization and neighbouring areas.

今後の研究の推進方策

(a) We will explore the computation of error bounds for other families of conic feasibility problems not yet covered by our past results.
(b) Explore further applications of error bounds in convergence analysis of algorithms.
(c) We will continue the investigation of geometric aspects of convex cones.
(d) Present our findings at conferences and visit research collaborators for in-depth discussions.

次年度使用額が生じた理由

Although the pandemic situation considerably improved in comparison with the previous fiscal years, travelling was still not easy and some of our research meetings got postponed. For the next fiscal year, we plan to use the remaining budget to visit research collaborators in order to advance the topics of this project.

  • 研究成果

    (17件)

すべて 2023 2022 その他

すべて 国際共同研究 (5件) 雑誌論文 (9件) (うち国際共著 5件、 査読あり 9件、 オープンアクセス 4件) 学会発表 (3件) (うち国際学会 1件、 招待講演 1件)

  • [国際共同研究] Curtin University/UNSW/Monash University(オーストラリア)

    • 国名
      オーストラリア
    • 外国機関名
      Curtin University/UNSW/Monash University
  • [国際共同研究] University of Sao Paulo/State University of Campinas(ブラジル)

    • 国名
      ブラジル
    • 外国機関名
      University of Sao Paulo/State University of Campinas
  • [国際共同研究] Hong Kong Polytechnic University(中国)

    • 国名
      中国
    • 外国機関名
      Hong Kong Polytechnic University
  • [国際共同研究] University of Coimbra(ポルトガル)

    • 国名
      ポルトガル
    • 外国機関名
      University of Coimbra
  • [国際共同研究] UNC at Chapel Hill(米国)

    • 国名
      米国
    • 外国機関名
      UNC at Chapel Hill
  • [雑誌論文] Hyperbolicity cones are amenable2023

    • 著者名/発表者名
      Lourenco Bruno F.、Roshchina Vera、Saunderson James
    • 雑誌名

      Mathematical Programming

      巻: - ページ: -

    • DOI

      10.1007/s10107-023-01958-0

    • 査読あり / オープンアクセス / 国際共著
  • [雑誌論文] Automorphisms of Rank-One Generated Hyperbolicity Cones and Their Derivative Relaxations2023

    • 著者名/発表者名
      Ito Masaru、Lourenco Bruno F.
    • 雑誌名

      SIAM Journal on Applied Algebra and Geometry

      巻: 7 ページ: 236~263

    • DOI

      10.1137/22M1513964

    • 査読あり
  • [雑誌論文] Random projections of linear and semidefinite problems with linear inequalities2023

    • 著者名/発表者名
      Poirion Pierre-Louis、Lourenco Bruno F.、Takeda Akiko
    • 雑誌名

      Linear Algebra and its Applications

      巻: 664 ページ: 24~60

    • DOI

      10.1016/j.laa.2023.01.013

    • 査読あり
  • [雑誌論文] Self-dual polyhedral cones and their slack matrices2023

    • 著者名/発表者名
      Gouveia Joao、Lourenco Bruno F.
    • 雑誌名

      SIAM Journal on Matrix Analysis (accepted)

      巻: - ページ: -

    • 査読あり / 国際共著
  • [雑誌論文] Convergence Analysis under Consistent Error Bounds2022

    • 著者名/発表者名
      Liu Tianxiang、Lourenco Bruno F.
    • 雑誌名

      Foundations of Computational Mathematics

      巻: - ページ: -

    • DOI

      10.1007/s10208-022-09586-4

    • 査読あり
  • [雑誌論文] Amenable Cones Are Particularly Nice2022

    • 著者名/発表者名
      Lourenco Bruno F.、Roshchina Vera、Saunderson James
    • 雑誌名

      SIAM Journal on Optimization

      巻: 32 ページ: 2347~2375

    • DOI

      10.1137/20M138466X

    • 査読あり / オープンアクセス / 国際共著
  • [雑誌論文] Error bounds, facial residual functions and applications to the exponential cone2022

    • 著者名/発表者名
      Lindstrom Scott B.、Lourenco Bruno F.、Pong Ting Kei
    • 雑誌名

      Mathematical Programming

      巻: - ページ: -

    • DOI

      10.1007/s10107-022-01883-8

    • 査読あり / オープンアクセス / 国際共著
  • [雑誌論文] A simplified treatment of Ramana’s exact dual for semidefinite programming2022

    • 著者名/発表者名
      Lourenco Bruno F.、Pataki Gabor
    • 雑誌名

      Optimization Letters

      巻: 17 ページ: 219~243

    • DOI

      10.1007/s11590-022-01898-2

    • 査読あり / 国際共著
  • [雑誌論文] A limiting analysis on regularization of singular SDP and its implication to infeasible interior-point algorithms2022

    • 著者名/発表者名
      Tsuchiya Takashi、Lourenco Bruno F.、Muramatsu Masakazu、Okuno Takayuki
    • 雑誌名

      Mathematical Programming

      巻: - ページ: -

    • DOI

      10.1007/s10107-022-01891-8

    • 査読あり / オープンアクセス
  • [学会発表] 自己双対多面錐のスラック行列について2022

    • 著者名/発表者名
      Lourenco Bruno F.
    • 学会等名
      数理最適化:モデル,理論,アルゴリズ
  • [学会発表] Koans of Cones: self-dual polyhedra2022

    • 著者名/発表者名
      Lourenco Bruno F.
    • 学会等名
      Matrix workshop on Convexity, Geometry and Computation
    • 国際学会 / 招待講演
  • [学会発表] 双曲錐の自己同型群について2022

    • 著者名/発表者名
      Lourenco Bruno F.
    • 学会等名
      最適化:モデリングとアルゴリズム

URL: 

公開日: 2023-12-25  

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