Methods for Complementarity and Related Problems

• Project/Area Number: 22500256
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Statistical science
• Research Institution: Nanzan University (2013); Kyoto University (2010-2012)
• Principal Investigator: FUKUSHIMA Masao 南山大学, 情報理工学部, 教授 (30089114)
• Project Period (FY): 2010-04-01 – 2014-03-31
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 相補性 / 最適化問題 / 均衡問題 / ゲーム理論 / 変分不等式 / 2次錐計画問題 / 確率的相補性問題 / 均衡制約付き最適化問題

Research Abstract

Complementarity is one of the most fundamental concepts in mathematical optimization, which plays an essentially important role in the optimality conditions of optimization problems and the formulation of various equilibrium problems. In this study, we have developed practical methods with a solid theoretical basis, for complementarity and related problems including eigenvalue complementarity problems, optimization problems with second-order cone complementarity constraints, nonlinear second-order cone programming problems, Nash equilibrium problems, generalized Nash equilibrium problems, and multi-leader-follower games.

Research Products

• [Journal Article] A globalized Newton method for the computation of normalized Nash equilibria (2013)
  • Author(s): A. Dreves, A. von Heusinger, C. Kanzow and M. Fukushima
  • Journal Title: Journal of Global Optimization Volume: Vol.56 Issue: 2 Pages: 327-340
  • DOI: 10.1007/s10898-011-9824-9
  • Peer Reviewed
• [Journal Article] Existence, uniqueness, and computation of robust Nash equilibria in a Class of multi-leader-follower games (2013)
  • Author(s): M. Hu and M. Fukushima
  • Journal Title: SIAM Journal on Optimization Volume: 23 Issue: 2 Pages: 894-916
  • DOI: 10.1137/120863873
  • Peer Reviewed
• [Journal Article] SDP reformulation for robust optimization problems based on nonconvex QP duality (2013)
  • Author(s): R. Nishimura, S. Hayashi and M. Fukushima
  • Journal Title: Computational Optimization and Applications Volume: Vol.55 Issue: 1 Pages: 21-47
  • DOI: 10.1007/s10589-012-9520-9
  • Peer Reviewed
• [Journal Article] A smoothing SQP method for mathematical programs with linear second- order cone complementarity constraints (2013)
  • Author(s): H. Yamamura, T. Okuno, S. Hayashi and M. Fukushima
  • Journal Title: Pacific Journal of Optimization Volume: Vol.9 Pages: 345-372
  • URL: http://www.ybook.co.jp/online2/pjov9.html
  • Peer Reviewed
• [Journal Article] Establishing Nash equilibrium of the manufacturer-supplier game in supply chain management (2013)
  • Author(s): J. Ang, M. Fukushima, F. Meng, T. Noda and J. Sun
  • Journal Title: Journal of Global Optimization Volume: Vol.56 Issue: 4 Pages: 1297-1312
  • DOI: 10.1007/s10898-012-9894-3
  • Peer Reviewed
• [Journal Article] 相補性制約をもつ非線形2次錐計画問題に対する平滑化法とスマートハウス運転計画問題への適用 (2013)
  • Author(s): 高須啓介, 田中洋一, 福嶋雅夫
  • Journal Title: システム制御情報学会論文誌 Volume: 第26巻 Pages: 34-44
  • NAID: 10031165972
  • URL: https://www.jstage.jst.go.jp/article/iscie/26/1/26_34/_pdf
  • Peer Reviewed
• [Journal Article] Rank-one solutions for homogeneous linear matrix equations over the positive semidefinite cone (2013)
  • Author(s): Y.B. Zhao and M. Fukushima
  • Journal Title: Applied Mathematics and Computation Volume: Vol.219 Issue: 10 Pages: 5569-5583
  • DOI: 10.1016/j.amc.2012.11.022
  • Peer Reviewed
• [Journal Article] 相補性制約をもつ非線形2次錐計画問題に対する平滑化法とスマートハウス運転計画問題への適用 (2013)
  • Author(s): 高須啓介，田中洋一，福嶋雅夫
  • Journal Title: システム制御情報学会論文誌 Volume: 26 Pages: 34-44
  • NAID: 10031165972
  • Peer Reviewed
• [Journal Article] A smoothing SQP method for mathematical programs with linear second-order cone complementarity constraints (2013)
  • Author(s): H. Yamamura, T. Okuno, S. Hayashi, M. Fukushima
  • Journal Title: Pacific Journal of Optimization Volume: 9 Pages: 345-372
  • Peer Reviewed
• [Journal Article] SDP reformulation for robust optimization problems based on nonconvex QP duality (2013)
  • Author(s): R. Nishimura, S. Hayashi, M. Fukushima
  • Journal Title: Computational Optimization and Applications Volume: 55 Pages: 21-47
  • Peer Reviewed
• [Journal Article] Differentiable exact penalty functions for nonlinear second-order cone programs (2012)
  • Author(s): E.H. Fukuda, P.J.S. Silva and M. Fukushima
  • Journal Title: SIAM Journal on Optimization Volume: Vol.22 Issue: 4 Pages: 1607-1633
  • DOI: 10.1137/110852401
  • Peer Reviewed
• [Journal Article] A regularized explicit exchange method for semi-infinite programs with an infinite number of conic constraints (2012)
  • Author(s): T. Okuno, S. Hayashi and M. Fukushima
  • Journal Title: SIAM Journal on Optimization Volume: Vol.22 Issue: 3 Pages: 1009-1028
  • DOI: 10.1137/110839631
  • NAID: 120004920429
  • Peer Reviewed
• [Journal Article] Variational inequality formulation of the asymmetric eigenvalue complementarity problem and its solution by means of gap functions (2012)
  • Author(s): C.P. Bras, M. Fukushima, J.J. Judice and S.S. Rosa
  • Journal Title: Pacific Journal of Optimization Volume: Vol.8 Pages: 197-215
  • URL: http://www.ybook.co.jp/online2/pjov6-1.html
  • Peer Reviewed
• [Journal Article] Smoothing approach to Nash equilibrium formulations for a class of equilibrium problems with shared complementarity constraints (2012)
  • Author(s): M. Hu, M. Fukushima
  • Journal Title: Computational Optimization and Applications Volume: 52 Issue: 2 Pages: 415-437
  • DOI: 10.1007/s10589-011-9416-0
  • Peer Reviewed
• [Journal Article] Semidefinite complementarity reformulation for robust Nash equilibrium problems with Euclidean uncertainty sets (2012)
  • Author(s): R. Nishimura, S. Hayashi and M. Fukushima
  • Journal Title: Journal of Global Optimization Volume: Vol.53 Issue: 1 Pages: 107-120
  • DOI: 10.1007/s10898-011-9719-9
  • Peer Reviewed
• [Journal Article] Newton's method for computing a normalized equilibrium in the gener- alized Nash game through fixed point formulation (2012)
  • Author(s): A. von Heusinger, C. Kanzow and M. Fukushima
  • Journal Title: Mathematical Programming Volume: Vol.132 Issue: 1-2 Pages: 99-123
  • DOI: 10.1007/s10107-010-0386-2
  • Peer Reviewed
• [Journal Article] SOR- and Jacobi-type iterative methods for solving l_1-l_2 problems by way of Fenchel duality (2012)
  • Author(s): M. Fukushima
  • Journal Title: Optimization Letters Volume: Vol.6 Issue: 4 Pages: 679-686
  • DOI: 10.1007/s11590-011-0292-4
  • Peer Reviewed
• [Journal Article] Variational inequality formulation of the asymmetric eigenvalue complementarity problem and its solution by means of gap functions (2012)
  • Author(s): C. Bras
  • Journal Title: Pacific Journal of Optimization Volume: 8 Pages: 197-215
  • Peer Reviewed
• [Journal Article] Variational inequality formulation of a class of multi-leader-follower games (2011)
  • Author(s): M. Hu and M. Fukushima
  • Journal Title: Journal of Optimization Theory and Applications Volume: Vol.151 Issue: 3 Pages: 455-473
  • DOI: 10.1007/s10957-011-9901-8
  • NAID: 120003573888
  • Peer Reviewed
• [Journal Article] Pricing American options with uncertain volatility through stochastic linear comple- mentarity models (2011)
  • Author(s): K. Hamatani and M. Fukushima
  • Journal Title: Computational Optimi- zation and Applications Volume: Vol.50 Issue: 2 Pages: 263-286
  • DOI: 10.1007/s10589-010-9344-4
  • Peer Reviewed
• [Journal Article] Restricted generalized Nash equilibria and controlled penalty algorithm (2011)
  • Author(s): M. Fukushima
  • Journal Title: Computational Management Science Volume: Vol.8 Issue: 3 Pages: 201-218
  • DOI: 10.1007/s10287-009-0097-4
  • NAID: 120003238946
  • Peer Reviewed
• [Journal Article] Parametrized variational inequality ap- proaches to generalized Nash equilibrium problems with shared constraints (2011)
  • Author(s): K. Nabetani, P. Tseng and M. Fukushima
  • Journal Title: Computational Optimization and Applications Volume: Vol.48 Issue: 3 Pages: 423-452
  • DOI: 10.1007/s10589-009-9256-3
  • Peer Reviewed
• [Journal Article] Smoothing method for mathematical programs with symmetric cone complementarity constraints (2011)
  • Author(s): T. Yan and M. Fukushima
  • Journal Title: Optimization Volume: Vol.60 Issue: 1-2 Pages: 113-128
  • DOI: 10.1080/02331934.2010.541458
  • Peer Reviewed
• [Journal Article] Smoothing method for mathematical programs with symmetric cone complementarity constraints (2011)
  • Author(s): T.Yan, M.Fukushima
  • Journal Title: Optimization Volume: 60 Pages: 113-128
  • Peer Reviewed
• [Journal Article] Stochastic equilibrium problems and stochastic mathematical programs with equilibrium constraints : A survey (2010)
  • Author(s): G.H. Lin and M. Fukushima
  • Journal Title: Pacific Journal of Optimization Volume: Vol.6 Pages: 455-482
  • URL: http://www.ybook.co.jp/online2/pjov6-1.html
  • Peer Reviewed
• [Journal Article] Stochastic equilibrium problems and stochastic mathematical programs with equilibrium constraints : A survey (2010)
  • Author(s): G.H.Lin, M.Fukushima
  • Journal Title: Pacific Journal of Optimization Volume: 6 Pages: 455-482
  • Peer Reviewed
• [Journal Article] Gap function approach to the generalized Nash equilibrium problem (2010)
  • Author(s): K. Kubota, M.Fukushima
  • Journal Title: Journal of Optimization Theory and Applications Volume: 144 Pages: 511-531
  • Peer Reviewed
• [Presentation] ナッシュ均衡問題とその拡張-定式化と計算手法- (2013)
  • Author(s): 福嶋雅夫
  • Organizer: 情報学シンポジウム
  • Place of Presentation: 京都大学, 京都市
  • Year and Date: 2013-12-26
• [Presentation] Equilibrium Problems with Equilibrium Constraints and Multi- Leader-Follower Games (2013)
  • Author(s): M. Fukushima
  • Organizer: The Ninth Inter- national Conference on Optimization : Techniques and Applications (ICOTA9)
  • Place of Presentation: Taipei, Taiwan
  • Year and Date: 2013-12-14
• [Presentation] Formulation and Computation of Robust Nash Equilibria in Multi-Leader-Follower Games (2013)
  • Author(s): M. Fukushima
  • Organizer: The Eighth International Conference on Nonlinear Analysis and Convex Analysis (NACA2013)
  • Place of Presentation: Hirosaki, Japan
  • Year and Date: 2013-08-03
• [Presentation] Formulation and Computation of Robust Nash Equilibria in Multi-Leader-Follower Games (2013)
  • Author(s): M. Fukushima
  • Organizer: The 8th International Conference on Nonlinear Analysis and Convex Analysis
  • Place of Presentation: 弘前大学
  • Invited
• [Presentation] Equilibrium Problems with Equilibrium Constraints and Multi-Leader-Follower Games (2013)
  • Author(s): M. Fukushima
  • Organizer: The 9th International Conference on Optimization: Techniques and Applications
  • Place of Presentation: Taipei, Taiwan
  • Invited
• [Presentation] ナッシュ均衡問題とその拡張：定式化と計算手法 (2013)
  • Author(s): 福嶋雅夫
  • Organizer: 情報学シンポジウム
  • Place of Presentation: 京都大学
  • Invited
• [Presentation] Generalized Nash Equilibrium Problems (2012)
  • Author(s): M. Fukushima
  • Organizer: The IMPA–60 Years Conference
  • Place of Presentation: Rio de Janeiro, Brazil
  • Year and Date: 2012-10-08
• [Presentation] Robust Nash Equilibrium in a Class of Multi-Leader-Follower Games (2012)
  • Author(s): M. Fukushima
  • Organizer: The 25th European Conference on Opera- tional Research (EURO XXV)
  • Place of Presentation: Vilnius, Lithuania
  • Year and Date: 2012-06-09
• [Presentation] Smoothing Approach to Equilibrium Problems with Shared Comple- mentarity Constraints (2012)
  • Author(s): M. Fukushima
  • Organizer: The Third Con- ference on Optimization Methods and Software
  • Place of Presentation: Chania, Greece
  • Year and Date: 2012-05-17
• [Presentation] Smoothing Approach to Equilibrium Problems with Shared Complementarity Constraints (2012)
  • Author(s): M. Fukushima
  • Organizer: The 3rd Conference on Optimization Methods and Software
  • Place of Presentation: Chania, Greece
  • Invited
• [Presentation] Robust Nash Equilibrium in a Class of Multi-Leader-Follower Games (2012)
  • Author(s): M. Fukushima
  • Organizer: The 25th European Conference on Operational Research
  • Place of Presentation: Vilnius, Lithuania
  • Invited
• [Presentation] Row Action Methods for Solving L1-L2 Optimization Problems (2011)
  • Author(s): M. Fukushima
  • Organizer: The Eighth International Conference on Numerical Optimization and Numerical Linear Algebra (ICNONLA 2011)
  • Place of Presentation: Xiamen, China
  • Year and Date: 2011-11-08
• [Presentation] Row Action Methods for Solving L1-L2 Optimization Problems (2011)
  • Author(s): M.Fukushima
  • Organizer: The 8th International Conference on Numerical Optimization and Numerical Linear Algebra
  • Place of Presentation: Xiamen, China
  • Year and Date: 2011-11-08
• [Presentation] SOR-type an Jacobi-type Iterative Methods for Solving L1-L2 Problems by Way of Fenchel Duality (2011)
  • Author(s): M. Fukushima
  • Organizer: The Third Alicante-Limoge-Elche Meeting on Optimization (III ALEL)
  • Place of Presentation: Castro Urdiales, Spain
  • Year and Date: 2011-06-25
• [Presentation] SOR-type and Jacobi-type Iterative Methods for Solving L1-L2 Problems by Way of Fenchel Duality (2011)
  • Author(s): M.Fukushima
  • Organizer: The III ALEL Meeting on Optimization
  • Place of Presentation: Castro Urdiales, Spain
  • Year and Date: 2011-06-25
• [Presentation] A Brief Overview of Stochastic Equilibrium Problems and Stochastic Mathematical Programs with Equilibrium Constraints (2010)
  • Author(s): M. Fukushima
  • Organizer: The Eighth International Conference on Optimization : Techniques ad Applications (ICOTA8)
  • Place of Presentation: Shanghai, China
  • Year and Date: 2010-12-12
• [Presentation] A Brief Overview of Stochastic Equilibrium Problems and Stochastic Mathematical Programs with Equilibrium Constraints (2010)
  • Author(s): M.Fukushima
  • Organizer: The 8th International Conference on Optimization : Techniques and Application(ICOTA8)
  • Place of Presentation: 中国・上海・復旦大学(招待講演)
  • Year and Date: 2010-12-12
• [Presentation] Parametrized Variational Inequality Approaches to Generalized Nash Equilibrium Problems with Shared Constraints (2010)
  • Author(s): M. Fukushima
  • Organizer: The Second South Pacific Conference on Mathematics (SPCM 2010)
  • Place of Presentation: Noumea, New Caledonia
  • Year and Date: 2010-09-02
• [Presentation] Generalized Nash Games and Variational Inequalities, The International Conference on Optimization (2010)
  • Author(s): M. Fukushima
  • Organizer: Simulation and Control (ICOSC 2010)
  • Place of Presentation: Ulaanbaatar, Mongolia
  • Year and Date: 2010-07-25
• [Presentation] Game Theory and Variational Inequalities–A Tutorial (2010)
  • Author(s): M. Fukushima
  • Organizer: International Conference on Optimization and Control (ICOCO 2010)
  • Place of Presentation: Guiyang, China
  • Year and Date: 2010-07-19
• [Remarks]
  • URL: http://www.seto.nanzan-u.ac.jp/~fuku/