Methods for Variational Inequalities and Related Problems

• Project/Area Number: 26330029
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical informatics
• Research Institution: Nanzan University
• Principal Investigator: Fukushima Masao 南山大学, 理工学部, 教授 (30089114)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 均衡問題 / 最適化問題 / 変分不等式 / 相補性問題 / ゲーム理論 / 最適化

Outline of Final Research Achievements

Variational inequalities play an important role in mathematical modeling of equilibrium problems that arise in such diverse areas as economics, transportation, finance and mechanics. The purpose of this research is to develop practical methods for problems closely related to variational inequalities, including complementarity problems, optimization problems, and problems in game theory. Specifically, in this research, we developed methods for eigenvalue complementarity problems, multi-leader-follower games, and conic optimization problems such as nonlinear semidefinite programs and nonlinear second-order cone programs.

Research Products

• [Int'l Joint Research] University of Coimbra(ポルトガル)
• [Int'l Joint Research] ＩＭＰＡ(ブラジル)
• [Int'l Joint Research] Instituto Politecnico de Tomar/Instituto de Telecommunicacoes(ポルトガル)
• [Int'l Joint Research] Virginia Tech(米国)
• [Int'l Joint Research] University of Coimbra(ポルトガル)
• [Int'l Joint Research] Instituto de Mathematica Pura e Aplicada(ブラジル)
• [Journal Article] Optimality conditions for problems over symmetric cones and a simple augmented Lagrangian method (2018)
  • Author(s): B.F. Lourenco, E.H. Fukuda, M. Fukushima
  • Journal Title: Mathematics of Operations Research Volume: 印刷中
  • Peer Reviewed / Open Access
• [Journal Article] A note on the squared slack variables technique for nonlinear optimization (2017)
  • Author(s): E.H. Fukuda, M. Fukushima
  • Journal Title: Journal of the Operations Research Society of Japan Volume: 60 Pages: 262-270
  • NAID: 130005874255
  • Peer Reviewed / Open Access
• [Journal Article] Optimality conditions for nonlinear semidefinite programming via squared slack variables (2017)
  • Author(s): Bruno Figueira Lourenco, Ellen Hidemi Fukuda and Masao Fukushima
  • Journal Title: Mathematical Programming Volume: 出版予定 Issue: 1-2 Pages: 177-200
  • DOI: 10.1007/s10107-016-1040-4
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] The second-order cone eigenvalue complementarity problem (2016)
  • Author(s): L.M. Fernandes, M. Fukushima, J.J. Judice and H.D. Sherali
  • Journal Title: Optimization Methods and Software Volume: 31 Issue: 1 Pages: 24-52
  • DOI: 10.1080/10556788.2015.1040156
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] The use of squared slack variables in nonlinear second-order cone programming (2016)
  • Author(s): Ellen Hidemi Fukuda and Masao Fukushima
  • Journal Title: Journal of Optimization Theory and Applications Volume: 出版予定 Issue: 2 Pages: 394-418
  • DOI: 10.1007/s10957-016-0904-3
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] On the quadratic eigenvalue complementarity problem over a general convex cone (2015)
  • Author(s): C.P. Bras, M. Fukushima, A.N. Iusem and J.J. Judice
  • Journal Title: Applied Mathematics and Computation Volume: 271 Pages: 594-608
  • DOI: 10.1016/j.amc.2015.09.014
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Multi-leader-follower games: Models, methods and applications (2015)
  • Author(s): M. Hu and M. Fukushima
  • Journal Title: Journal of the Operations Research Society of Japan Volume: 58 Pages: 1-23
  • NAID: 130005067215
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] On the computation of all eigenvalues for the eigenvalue complementarity problem (2014)
  • Author(s): L.M. Fernandes, J.J. Judice, H.D. Sherali, and M. Fukushima
  • Journal Title: Journal of Global Optimization Volume: 56 Issue: 2-3 Pages: 307-326
  • DOI: 10.1007/s10898-014-0165-3
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] A regularized outer approximation method for monotone semi-infinite variational inequality problems (2014)
  • Author(s): M. Kono and M. Fukushima
  • Journal Title: Pacific Journal of Optimization Volume: 10 Pages: 735-748
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] On the symmetric quadratic eigenvalue complementarity problem (2014)
  • Author(s): L.M. Fernandes, J.J. Judice, M. Fukushimaand A.N. Iusem
  • Journal Title: Optimization Methods & Software Volume: 29 Issue: 4 Pages: 751-770
  • DOI: 10.1080/10556788.2013.854359
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Presentation] マルチリーダー・フォロワーゲームに対するGauss-Seidel法 (2018)
  • Author(s): 堀篤史，福島雅夫
  • Organizer: 日本オペレーションズ・リサーチ学会2018年春季研究発表会
• [Presentation] Maintenance scheduling of flood control plant under uncertainty based on multi-objective optimization (2018)
  • Author(s): I. Takami, M. Fukushima, F. Yamada, S. Inagaki
  • Organizer: The 7th International Conference on Industrial Technology and Management (ICITM 2018)
  • Int'l Joint Research
• [Presentation] Second-Order Conditions for Nonlinear Semidefinite Optimization Problems via Slack Variables Approach (2016)
  • Author(s): E.H. Fukuda, B.F. Lourenco and M. Fukushima
  • Organizer: The Fifth International Conference on Continuous Optimization
  • Place of Presentation: Tokyo, Japan
  • Year and Date: 2016-08-06
  • Int'l Joint Research
• [Presentation] A Gauss-Seidel Method for Multi-Leader-Follower Games (2016)
  • Author(s): A. Hori and M. Fukushima
  • Organizer: The Fifth International Conference on Continuous Optimization
  • Place of Presentation: Tokyo, Japan
  • Year and Date: 2016-08-06
  • Int'l Joint Research
• [Presentation] マルチ・リーダー・フォロワーゲーム -- 連続最適化の観点から -- (2016)
  • Author(s): 福嶋雅夫
  • Organizer: 日本オペレーションズ・リサーチ学会春季研究発表会
  • Place of Presentation: 横浜市
  • Year and Date: 2016-03-18
  • Invited
• [Presentation] Go around Complementarity (2015)
  • Author(s): M. Fukushima
  • Organizer: The 22nd International Symposium on Mathematical Programming
  • Place of Presentation: Pittsburgh, USA
  • Year and Date: 2015-07-15
  • Int'l Joint Research / Invited
• [Presentation] Squared Slack Variables in Nonlinear Second-Order Cone Programming (2015)
  • Author(s): M. Fukushima
  • Organizer: International Conference on Variational Analysis, Optimization and Quantitative Finance
  • Place of Presentation: Limoges, France
  • Year and Date: 2015-05-19
  • Int'l Joint Research / Invited
• [Presentation] Some results in multi-leader-follower games (2014)
  • Author(s): M. Fukushima
  • Organizer: Optimization 2014
  • Place of Presentation: Guimaraes, Portugal
  • Year and Date: 2014-07-29
  • Invited