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Methods for Robust Optimization and Related Problems

Research Project

Project/Area Number 17360042
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionKyoto University

Principal Investigator

FUKUSHIMA Masao  Kyoto University, 大学院・情報学研究科, 教授 (30089114)

Co-Investigator(Kenkyū-buntansha) CHIN Syoukun  弘前大学, 理工学部, 教授 (70304251)
YAMASHITA Nobuo  京都大学, 大学院・情報学研究科, 准教授 (30293898)
HAYASHI Shunsuke  京都大学, 大学院・情報学研究科, 助教 (20444482)
Project Period (FY) 2005 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥16,590,000 (Direct Cost: ¥14,400,000、Indirect Cost: ¥2,190,000)
Fiscal Year 2008: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2007: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2006: ¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2005: ¥3,500,000 (Direct Cost: ¥3,500,000)
Keywords数理工学 / システム工学 / 最適化 / アルゴリズム / 数理計画 / 不確実性 / 均衡モデル / ロバスト
Research Abstract

所与の制約条件のもとで,ある評価規範を最大化あるいは最小化する問題を数理的に表現した最適化モデルにおいて,データの予測が困難であるなど,様々な不確実さをどのように取り扱うか非常に重要な課題である.本研究では,確率的あるいは非確率的な不確実性を含む最適化問題とそれに関連する諸問題に対して,ロバスト(頑健な)最適化を達成するための,堅固な理論的基盤に立脚した実用的な手法を開発した.

Report

(5 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (71 results)

All 2009 2008 2007 2006 2005 Other

All Journal Article (61 results) (of which Peer Reviewed: 34 results) Presentation (8 results) Book (1 results) Remarks (1 results)

  • [Journal Article] Robust solution of monotone stochastic linear complementarity problems2009

    • Author(s)
      X. Chen, C. Zhang, M. Fukushima
    • Journal Title

      matical Programming Vol.117

      Pages: 51-80

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Solving stochastic mathematical programs with equilibrium constraints via approximation and smoothing implicit programming with penalization2009

    • Author(s)
      G.H. Lin, X. Chen and M. Fukushima
    • Journal Title

      Mathematical Programming Vol.116

      Pages: 343-368

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Robust Nash equilibria in N-person non-cooperative game2009

    • Author(s)
      R. Nishimura, S. Hayashi, M. Fukushima
    • Journal Title

      Pacific Journal of Optimization (掲載決定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 確率計画法によるコージェネレーションシステムの運用最適化2009

    • Author(s)
      田中洋一, 福島雅夫
    • Journal Title

      電気学会論文誌B編 (掲載決定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Monte Carlo and quasi-Monte Carlo sampling methods for a class of stochastic mathematical programs with equilibrium constraints2008

    • Author(s)
      G.H. Lin, H. Xu, and M. Fukushima
    • Journal Title

      Mathematical Methods of Operations Research Vol.67

      Pages: 423-441

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Portfolio selection with uncertain exit time: A robust CVaR approach2008

    • Author(s)
      D.S. Huang, S.S. Zhu, F.J. Fabozzi and M. Fukushima
    • Journal Title

      Journal of Economic Dynamics and Control Vol.32

      Pages: 594-623

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Portfolio selection with uncertain exit time : A robust CVaR approach2008

    • Author(s)
      D. S. Huang, S. S. Zhu, F. J. Fabozzi, M. Fukushima
    • Journal Title

      Journal of Economic Dynamics and Control 32

      Pages: 594-623

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Monte Carlo and quasi-Monte Carlo sampling methods for a class of stochastic mathematical programs with2008

    • Author(s)
      G. H. Lin, H. Xu, M. Fukushima
    • Journal Title

      Mathematical Methods of Operations Research 67

      Pages: 423-441

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Evaluation of firm's loss due to incomplete information in real investment decision2008

    • Author(s)
      M. Nishihara and M. Fuklushima
    • Journal Title

      European Journal of Operational Research 188

      Pages: 569-585

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An implicit programming approach to the road pricing problem with nonadditive route costs2008

    • Author(s)
      R. P. Agdeppa, N. Yamashita and M. Fukushima
    • Journal Title

      Journal of Industrial and Management Optimization 4

      Pages: 183-197

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] New restricted NCP functions and their applications to stochastic NCP and stochastic MPEC2007

    • Author(s)
      G.H. Lin, X. Chen and M. Fukushima
    • Journal Title

      Optimization Vol.56

      Pages: 641-653

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Robust portfolio selection with uncertain exit time using worst-case VaR strategy2007

    • Author(s)
      D.S. Huang, F.J. Fabozzi and M. Fukushima
    • Journal Title

      Operations Research Letters Vol.35

      Pages: 627-635

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stochastic $R_0$ matrix linear complementarity problems2007

    • Author(s)
      H. Fang, X. Chen and M. Fukushima
    • Journal Title

      SIAM Journal on Optimization Vol.18

      Pages: 482-506

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] An SQP-type algorithm for nonlinear second-order cone programs2007

    • Author(s)
      H. Kato and M. Fukushima
    • Journal Title

      Optimization Letters Vol.1

      Pages: 129-144

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Second order cone programming formulations for robust multi-class classification2007

    • Author(s)
      P. Zhong and M. Fukushima
    • Journal Title

      Neural Computation Vol.19

      Pages: 258-282

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hybrid evolutionary algorithm for solving general variational inequality problems2007

    • Author(s)
      M. -A. majig, A. -R. Hedar and M. Fukushima
    • Journal Title

      Journal of Global Optimization 38

      Pages: 637-651

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A finite algorithm for almost linear complementarity problems2007

    • Author(s)
      Z. Wang and M. Fukushima
    • Journal Title

      Numerical Functional Analysis and Optimization 28

      Pages: 1387-1403

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A regularized nonsmooth Newton method for multi-class support vector machines2007

    • Author(s)
      P.Zhong, M.Fukushima
    • Journal Title

      Optimization Methods and Software 22・1

      Pages: 225-236

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Second order cone programming formulations for robust multi-class classification2007

    • Author(s)
      P.Zhong, M.Fukushima
    • Journal Title

      Neural Computation 19・1

      Pages: 258-282

    • Related Report
      2006 Annual Research Report
  • [Journal Article] An SQP-type algorithm for nonlinear second-order cone programs2007

    • Author(s)
      H.Kato, M.Fukushima
    • Journal Title

      Optimization Letters 1・2

      Pages: 129-144

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Parallelizable preprocessing method for multistage stochastic programming problems2006

    • Author(s)
      X.W. Liu and M. Fukushima
    • Journal Title

      Journal of Optimization Theory and Applications Vol.131

      Pages: 327-346

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] New reformulations for stochastic nonlinear complementarity problems2006

    • Author(s)
      G.H. Lin and M. Fukushima
    • Journal Title

      Optimization Methods, Software Vol.21

      Pages: 551-564

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A new multi-class support vector algorithm2006

    • Author(s)
      P.Zhong, M.Fukushima
    • Journal Title

      Optimization Methods and Software 21・3

      Pages: 359-372

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Hybrid approach with active set identification for mathematical programs with complementarity constraints2006

    • Author(s)
      G.H.Lin, M.Fukushima
    • Journal Title

      Journal of Optimization Theory and Applications 128・1

      Pages: 1-28

    • Related Report
      2006 Annual Research Report
  • [Journal Article] New reformulations for stochastic nonlinear complementarity problems2006

    • Author(s)
      G.H.Lin, M.Fukushima
    • Journal Title

      Optimization Methods and Software 21・4

      Pages: 551-564

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Expected residual minimization method for stochastic linear complementarity problems2005

    • Author(s)
      X. Chen and M. Fukushima
    • Journal Title

      Mathematics of Operations Research Vol.30

      Pages: 1022-1038

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Robust Nash equilibria and second-order cone complementarity problems2005

    • Author(s)
      S. Hayashi, N. Yamashita and M. Fukushima
    • Journal Title

      Journal of Nonlinear and Convex Analysis Vol.6

      Pages: 283-296

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Successive linearization methods for nonlinear semidefinite programs2005

    • Author(s)
      C. Kanzow, C. Nagel, H. Kato and M. Fukushima
    • Journal Title

      Computational Optimization and Applications Vol.31

      Pages: 251-273

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A combined smoothing and regularization method for monotone second-order cone complementarity problems2005

    • Author(s)
      S. Hayashi, N. Yamashita and M. Fukushima
    • Journal Title

      SIAM Journal on Optimization Vol.15

      Pages: 593-615

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Regularization method for stochastic mathematical programs with comple- mentarity constraints, European Series of Applied and Industrial Mathematics (ESAIM): Control2005

    • Author(s)
      G.H. Lin, and M. Fukushima
    • Journal Title

      Optimization and the Calculus of Variations (COCV) Vol.11

      Pages: 252-265

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A smoothing implicit programming approach for solving a class of stochastic generalized semi-infinite programming problems2005

    • Author(s)
      C. Ling, X. Chen, M. Fukushima, and L. Qi
    • Journal Title

      Pacific Journal of Optimization Vol.1

      Pages: 127-145

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A class of stochastic mathematical programs with complementarity constraints: Reformula- tions and algorithms2005

    • Author(s)
      G.H. Lin and M. Fukushima
    • Journal Title

      Journal of Industrial and Management Optimization Vol.1

      Pages: 99-122

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A matrix splitting method for symmetric affine second-order cone complementarity prob-lems2005

    • Author(s)
      S. Hayashi, T. Yamaguchi, N. Yamashita and M. Fukushima
    • Journal Title

      Journal of Computational and Applied Mathematics Vol.175

      Pages: 335-353

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A modified relaxation scheme for mathematical programs with complementarity constraints2005

    • Author(s)
      G.H.Lin, M.Fukushima
    • Journal Title

      Annals of Operations Research 133・1

      Pages: 63-84

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games2005

    • Author(s)
      J.-S.Pang, M.Fukushima
    • Journal Title

      Computational Management Science 2・1

      Pages: 21-56

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A matrix splitting method for symmetric affine second-order cone complementarity problems2005

    • Author(s)
      S.Hayashi, T.Yamaguchi, N.Yamashita, M.Fukushima
    • Journal Title

      Journal of Computational and Applied Mathematics 175・2

      Pages: 335-353

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A class of stochastic mathematical programs with complementarity constraints : Reformulations and algorithms2005

    • Author(s)
      G.H.Lin, M.Fukushima
    • Journal Title

      Journal of Industrial and Management Optimization 1・1

      Pages: 99-122

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A trust region method for nonsmooth convex optimization2005

    • Author(s)
      N.Sagara, M.Fukushima
    • Journal Title

      Journal of Industrial and Management Optimization 1・2

      Pages: 171-180

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A smoothing implicit programming approach for solving a class of stochastic generalized semi-infinite programming problems2005

    • Author(s)
      C.Ling, X.Chen, M.Fukushima, L.Qi
    • Journal Title

      Pacific Journal of Optimization 1・1

      Pages: 127-145

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Regularization method for stochastic mathematical programs with complementarity constraints2005

    • Author(s)
      G.H.Lin, M.Fukushima
    • Journal Title

      European Series of Applied and Industrial Mathematics (ESAIM) : Control, Optimization and the Calculus of Variations (COCV) 11・2

      Pages: 252-265

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A combined smoothing and regularization method for monotone second-order cone complementarity problems2005

    • Author(s)
      S.Hayashi, N.Yamashita, M.Fukushima
    • Journal Title

      SIAM Journal on Optimization 15・2

      Pages: 593-615

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Successive linearization methods for nonlinear semidefinite programs2005

    • Author(s)
      C.Kanzow, C.Nagel, H.Kato, M.Fukushima
    • Journal Title

      Computational Optimization and Applications 31・3

      Pages: 251-273

    • Related Report
      2005 Annual Research Report
  • [Journal Article] 空港施設運用における効率とセキュリティの最適化2005

    • Author(s)
      熊野信太郎, 溝口正信, 滝根哲哉, 福島雅夫
    • Journal Title

      システム制御情報学会論文誌 18・4

      Pages: 146-155

    • NAID

      10015475917

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Robust Nash equilibria and second-order cone complementarity problems2005

    • Author(s)
      S.Hayashi, N.Yamashita, M.Fukushima
    • Journal Title

      Journal of Nonlinear and Convex Analysis 6・2

      Pages: 283-296

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On the level-boundedness of the natural residual function for variational inequality problems2005

    • Author(s)
      N.Yamashita, M.Fukushima
    • Journal Title

      Pacific Journal of Optimization 1・3

      Pages: 625-630

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Expected residual minimization method for stochastic linear complementarity problems2005

    • Author(s)
      X.Chen, M.Fukushima
    • Journal Title

      Mathematics of Operations Research 30・4

      Pages: 1022-1038

    • Related Report
      2005 Annual Research Report
  • [Journal Article] 確率計画法によるコージェネレーションシステムの運用最適化

    • Author(s)
      田中洋一, 福嶋雅夫
    • Journal Title

      電気学会論文誌 B (掲載決定)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the local convergence of semismooth Newton methods for linear and nonlinear second-order cone programs without strict complementarity

    • Author(s)
      C. Kanzow, I. Ferenczi and M. Fukushima
    • Journal Title

      SIAM Journal on Optimization (掲載決定)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Worst-case conditional Value-at-Risk with applica- tion to robust portfolio management

    • Author(s)
      S.S. Zhu and M. Fukushima
    • Journal Title

      Operations Research (掲載決定)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Convex expected residual models for stochastic affine variational inequality problems and its application to the traffic equilibrium problem

    • Author(s)
      R.P. Agdeppa, N. Yamashita and M. Fukushima
    • Journal Title

      Pacific Journal of Optimization (掲載決定)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Robust Nash equilibria in N-person non-cooperative games : Unique- ness and reformulation

    • Author(s)
      R. Nishimura, S. Hayashi and M. Fukushima
    • Journal Title

      Pacific Journal of Optimization (掲載決定)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] An optimal design of collateralized mortgage obligation with PAC-companion structure using dynamic cash reserve

    • Author(s)
      D. S. Huang, Y. Kai, F. J. Fabozzi and M. Fukushima
    • Journal Title

      European Journal of Operational Research (掲載決定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Parallelizable preprocessing method for multistage stochastic programmming problems

    • Author(s)
      X. -W. Liu and M. Fukushima
    • Journal Title

      Journal of Optimization Theory and Applications (掲載決定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Solving stochastic mathematical programs with equilibrium constraints via approximation and smoothing implicit programming with penalization

    • Author(s)
      G.H.Lin, X.Chen, M.Fukushima
    • Journal Title

      Mathematical Programming (掲載決定)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Robust solution of stochastic matrix linear complementarity problems

    • Author(s)
      X.Chen, C.Zhang, M.Fukushima
    • Journal Title

      Mathematical Programming (掲載決定)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A class of gap functions for quasi-variational inequality problems

    • Author(s)
      M.Fukushima
    • Journal Title

      Journal of Industrial and Management Optimization (掲載決定)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Robust portfolio selection with uncertain exit time using worst-case VaR strategy

    • Author(s)
      D.S.Huang, F.J.Fabozzi, M.Fukushima
    • Journal Title

      Operations Research Letters (掲載決定)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Stochastic $R_O$ matrix linear complementarity problems

    • Author(s)
      H.Fang, X.Chen, M.Fukushima
    • Journal Title

      SIAM Journal on Optimization (掲載決定)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A mixed R&D projects and securities portfolio selection model

    • Author(s)
      Y.Fang, L.H.Chen, M.Fukushima
    • Journal Title

      European Journal of Operational Research (掲載決定)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] An optimal design of collateralized mortgage obligation with PAC-companion structure using dynamic cash reserve

    • Author(s)
      D.S.Huang, Y.Kai, F.J.Fabozzi, M.Fukushima
    • Journal Title

      European Journal of Operational Research (掲載決定)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Parallelizable preprocessing method for multistage stochastic programming problems

    • Author(s)
      X.W.Liu, M.Fukushima
    • Journal Title

      Journal of Optimization Theory and Applications (掲載決定)

    • Related Report
      2006 Annual Research Report
  • [Presentation] Restricted Generalized Nash Equilibria2008

    • Author(s)
      M. Fukushima
    • Organizer
      The Fourth Sino-Japanese Optimization Meeting (SJOM 2008)
    • Place of Presentation
      Tainan, Taiwan
    • Year and Date
      2008-08-27
    • Related Report
      2008 Final Research Report
  • [Presentation] Equilibrium Problems under Uncertainty2008

    • Author(s)
      M. Fukushima
    • Organizer
      International Confer- ence on Modeling, Computation and Optimization (ICMCO 2008),
    • Place of Presentation
      Indian Statistical Institute, Delhi Centre
    • Year and Date
      2008-01-09
    • Related Report
      2008 Final Research Report
  • [Presentation] Optimization Reformulation of Generalized Nash Equilibrium Problems2007

    • Author(s)
      M. Fukushima
    • Organizer
      The Sixth International Conference on Numerical Optimization and Numerical Linear Algebra (NLAO 2007)
    • Place of Presentation
      Urumqi, Xin-Jiang, China,
    • Year and Date
      2007-09-08
    • Related Report
      2008 Final Research Report
  • [Presentation] Semismooth Methods for Second-Order Cone Programs2007

    • Author(s)
      M. Fukushima
    • Organizer
      The Second International Conference on Optimization and Optimal Control
    • Place of Presentation
      Ulaanbaatar, Mongolia
    • Year and Date
      2007-07-17
    • Related Report
      2008 Final Research Report
  • [Presentation] A gap function for quasi variational inequalities and its application to generalized Nash equilibrium problems2007

    • Author(s)
      M. Fukushima
    • Organizer
      The Joint EUROPT-OMS Meeting
    • Place of Presentation
      Prague, Czech Republic,
    • Year and Date
      2007-07-04
    • Related Report
      2008 Final Research Report
  • [Presentation] A Gap Function for Quasi-Variational Inequalities and Its Application to Generalized Nash Equilibria2007

    • Author(s)
      M. Fukushima
    • Organizer
      International Conference on Nonsmooth and Variational Analysis in Sciences and Engineering (NVA 2007)
    • Place of Presentation
      Limoges, France
    • Year and Date
      2007-06-20
    • Related Report
      2008 Final Research Report
  • [Presentation] Semismooth methods for linear and nonlinear second-order cone programs2007

    • Author(s)
      M. Fukushima
    • Organizer
      The Fifth International Confer- ence on Nonlinear Analysis and Convex Analysis (NACA2007),
    • Place of Presentation
      National Tsing-Hua University, Taiwan,
    • Year and Date
      2007-05-31
    • Related Report
      2008 Final Research Report
  • [Presentation] Linear Complementarity Problems under Uncertainty2006

    • Author(s)
      M. Fukushima
    • Organizer
      The Inter- national Conference on Nonlinear Programming with Applications (NPA 2006)
    • Place of Presentation
      Shanghai, China
    • Year and Date
      2006-05-29
    • Related Report
      2008 Final Research Report
  • [Book] 数理計画法2008

    • Author(s)
      山下信雄・福嶋雅夫
    • Total Pages
      182
    • Publisher
      コロナ社
    • Related Report
      2008 Final Research Report
  • [Remarks]

    • URL

      http://www-optima.amp.i.kyoto-u.ac.jp/~fuku/

    • Related Report
      2008 Final Research Report

URL: 

Published: 2005-04-01   Modified: 2021-09-01  

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