Research on constraint qualification and solution method for set optimization programming

• Project/Area Number: 22540133
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Shimane University
• Principal Investigator: KUROIWA Daishi 島根大学, 総合理工学研究科, 教授 (40284020)
• Co-Investigator(Renkei-kenkyūsha): TANAKA Tamaki 新潟大学, 自然科学系, 教授 (10207110) ; YAMAUCHI Takamitsu 島根大学, 総合理工学研究科, 講師 (00403444) ; MATSUSHITA Shin-ya 秋田県立大学, システム科学技術学部, 助教 (20435449)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 集合値最適化 / 微分概念 / 多目的最適化 / 数理計画法 / 集合値計画法 / 埋め込み / 制約想定 / 双対理論 / 相対理論

Research Abstract

We study constraint qualification for optimization problems whose objective maps are set-valued maps based on criteria called `set optimization.’ We propose certain constraint qualifications for set optimization problems including a set optimization problem whose objective and constraint functions are set -valued convex functions. Also we study solution methods for well-posed set optimization problems.

Research Products

• [Journal Article] Some constraint qualifications for quasiconvexvector-valued systems (2013)
  • Author(s): S. Suzuki and D. Kuroiwa
  • Journal Title: J. Global Optim Volume: 55 Pages: 539-548
  • NAID: 120005647345
  • Peer Reviewed
• [Journal Article] Optimality conditions for DC programming problems with reverse convex constraints (2013)
  • Author(s): Y. Saeki and D. Kuroiwa
  • Journal Title: Nonlinear Anal Volume: 80 Pages: 18-27
  • Peer Reviewed
• [Journal Article] Optimality conditions for DC programming problems with reverse convex constraints (2013)
  • Author(s): Saeki, Yusuke; Kuroiwa, Daishi
  • Journal Title: Nonlinear Anal. Volume: 80 Pages: 18-27
  • DOI: 10.1016/j.na.2012.11.025
  • Peer Reviewed
• [Journal Article] Some constraint qualifications for quasiconvex vector-valued systems (2013)
  • Author(s): Suzuki, Satoshi; Kuroiwa, Daishi
  • Journal Title: J. Global Optim. Volume: 55 Issue: 3 Pages: 539-548
  • DOI: 10.1007/s10898-011-9807-x
  • NAID: 120005647345
  • Peer Reviewed
• [Journal Article] On robust multiobjective optimization (2012)
  • Author(s): G.M. Lee and D. Kuroiwa
  • Journal Title: Vietnam J. Math Volume: 40 Pages: 305-317
  • Peer Reviewed
• [Journal Article] Necessary and sufficient conditions for some constraint qualifications in quasiconvex programming (2012)
  • Author(s): S. Suzuki and D. Kuroiwa
  • Journal Title: Nonlinear Analysis Volume: 75 Pages: 2851-2858
  • NAID: 120005647350
  • Peer Reviewed
• [Journal Article] Necessary and sufficient constraint qualification for surrogate duality (2012)
  • Author(s): S. Suzuki and D. Kuroiwa
  • Journal Title: J. Optim.Theory Appl Volume: 152 Pages: 366-377
  • NAID: 120005647346
  • Peer Reviewed
• [Journal Article] Necessary and sufficient conditions for some constraint qualifications in quasiconvex programming (2012)
  • Author(s): Suzuki, Satoshi; Kuroiwa, Daishi
  • Journal Title: Nonlinear Anal. Volume: 75 Issue: 5 Pages: 2851-2858
  • DOI: 10.1016/j.na.2011.11.025
  • NAID: 120005647350
  • Peer Reviewed
• [Journal Article] Necessary and sufficient constraint qualification for surrogate duality (2012)
  • Author(s): Suzuki, Satoshi; Kuroiwa, Daishi
  • Journal Title: J. Optim. Theory Appl. Volume: 152 Issue: 2 Pages: 366-377
  • DOI: 10.1007/s10957-011-9893-4
  • NAID: 120005647346
  • Peer Reviewed
• [Journal Article] On robust multiobjective optimization (2012)
  • Author(s): Kuroiwa, Daishi; Lee, Gue Myung
  • Journal Title: Vietnam J. Math. Volume: 40 Pages: 305-317
  • Peer Reviewed
• [Journal Article] A necessary and sufficient constraint qualification for DC programming problems with convex inequality constraints (2011)
  • Author(s): Y. Saeki, S. Suzuki and D. Kuroiwa
  • Journal Title: Sci. Math. Jpn Volume: 74 Pages: 49-54
  • NAID: 130007670099
  • Peer Reviewed
• [Journal Article] Nash equilibrium and saddle points for multifunctions, Commun (2011)
  • Author(s): P. G. Georgiev, T. Tanaka, D. Kuroiwa, and P. M. Pardalos
  • Journal Title: Commun. Math. Anal Volume: 10 Pages: 118-127
  • Peer Reviewed
• [Journal Article] Subdifferential calculus for a quasiconvex function with generator (2011)
  • Author(s): S. Suzuki and D. Kuroiwa
  • Journal Title: J. Math. Anal.Appl Volume: 384 Pages: 677-682
  • NAID: 120005647347
  • Peer Reviewed
• [Journal Article] On set containment characterization and constraint qualification for quasiconvex programming (2011)
  • Author(s): S. Suzuki and D. Kuroiwa
  • Journal Title: J. Optim. Theory Appl Volume: 149 Pages: 554-563
  • NAID: 120005647349
  • Peer Reviewed
• [Journal Article] Sandwich theorem for quasiconvex functions andits applications (2011)
  • Author(s): S. Suzuki and D. Kuroiwa
  • Journal Title: J. Math. Anal. Appl Volume: 379 Pages: 649-655
  • Peer Reviewed
• [Journal Article] Optimalityconditions and the basic constraintqualification for quasiconvex Programming (2011)
  • Author(s): S. Suzuki and D. Kuroiwa
  • Journal Title: Nonlinear Analysis Volume: 74 Pages: 1279-1285
  • Peer Reviewed
• [Journal Article] 準凸関数に対するサンドイッチ定理とその適用例 (2011)
  • Author(s): S. Suzuki and D. Kuroiwa
  • Journal Title: RIMS Kokyuroku Volume: 1755 Pages: 182-187
• [Journal Article] 凸不等式制約付き DC 計画問題における最弱の制約想定 (2011)
  • Author(s): S. Suzuki and D. Kuroiwa
  • Journal Title: RIMS Kokyuroku Volume: 1755 Pages: 204-209
• [Journal Article] Optimality conditions and the basic constraint qualification for quasiconvex programming (2011)
  • Author(s): S.Suzuki, D.Kuroiwa
  • Journal Title: Nonlinear Analysis : Theory, Methods & Applications Volume: 74 Issue: 4 Pages: 1279-1285
  • DOI: 10.1016/j.na.2010.09.066
  • NAID: 120005647351
  • Peer Reviewed
• [Journal Article] On set containment characterization and constraint qualification for quasiconvex programming (2011)
  • Author(s): S.Suzuki, D.Kuroiwa
  • Journal Title: Journal of Optimization Theory and Applications Volume: 149 Issue: 3 Pages: 554-563
  • DOI: 10.1007/s10957-011-9804-8
  • NAID: 120005647349
  • Peer Reviewed
• [Journal Article] Sandwich theorem for quasiconvex functions and its applications (2011)
  • Author(s): S.Suzuki, D.Kuroiwa
  • Journal Title: Journal of Mathematical Analysis and Applications Volume: 379 Issue: 2 Pages: 649-655
  • DOI: 10.1016/j.jmaa.2011.01.061
  • Peer Reviewed
• [Journal Article] Subdifferential calculus for a quasiconvex function with generator (2011)
  • Author(s): S.Suzuki, D.Kuroiwa
  • Journal Title: Journal of Mathematical Analysis and Applications Volume: 384 Issue: 2 Pages: 677-682
  • DOI: 10.1016/j.jmaa.2011.06.015
  • NAID: 120005647347
  • Peer Reviewed
• [Journal Article] A necessary and sufficient constraint qualification for DC programming problems with convex inequality constraints (2011)
  • Author(s): Y.Saeki, S.Suzuki, D.Kuroiwa
  • Journal Title: Scientiae Mathematicae Japonicae Volume: 74 Pages: 49-54
  • NAID: 130007670099
  • Peer Reviewed
• [Journal Article] Optimality conditions and the basic constraint qualification for quasicon vex programming (2011)
  • Author(s): Satoshi Suzuki, Daishi Kuroiwa
  • Journal Title: Nonlinear Anal. Volume: 74 Pages: 1279-1285
  • NAID: 120005647351
  • Peer Reviewed
• [Journal Article] Common fixed point theorems of Caristi type mappings with wdistance (2010)
  • Author(s): T. Obama and D. Kuroiwa
  • Journal Title: Sci. Math. Jpn Volume: 72 Pages: 41-48
  • NAID: 10026502006
  • Peer Reviewed
• [Journal Article] Observations of closed cone constraint qualification for quasiconvex programming (2010)
  • Author(s): S. Suzuki and D. Kuroiwa
  • Journal Title: Nonlinear analysis and convex analysis Pages: 321-326
  • Peer Reviewed
• [Journal Article] Common fixed point theorems of Caristi type mappings with w-distance (2010)
  • Author(s): Tomoaki Obama, Daishi Kuroiwa
  • Journal Title: Sci.Math.Jpn. Volume: 72 Pages: 41-48
  • NAID: 10026502006
  • Peer Reviewed
• [Journal Article] w-distanceを用いた共通不動点定理とその応用 (2010)
  • Author(s): Tomoaki Obama, Yuya Shiraishi, Daishi Kuroiwa
  • Journal Title: 数理解析研究所講究録 Volume: 1685 Pages: 231-236
• [Journal Article] 準凸計画問題における制約想定とその適用例 (2010)
  • Author(s): Satoshi Suzuki, Daishi Kuroiwa
  • Journal Title: 数理解析研究所講究録 Volume: 1685 Pages: 237-242
• [Journal Article] ベクトル値準凸制約をもつ最適化問題 (2010)
  • Author(s): Takuya Shimomura, Satoshi Suzuki, Daishi Kuroiwa
  • Journal Title: 数理解析研究所講究録 Volume: 1685 Pages: 243-248
• [Journal Article] Surrogate duality for robust optimization
  • Author(s): S. Suzuki, D. Kuroiwa and G.M. Lee
  • Journal Title: European Journal of Operational Research
  • NAID: 120005647348
  • Peer Reviewed
• [Journal Article] Set optimization with DC objective function
  • Author(s): D. Kuroiwa
  • Journal Title: Nonlinear Analysis and Convex Analysis
  • Peer Reviewed
• [Presentation] Set optimization - an embedding approach (2013)
  • Author(s): D. Kuroiwa
  • Organizer: Symposium on Set-valued Optimization
  • Place of Presentation: Halle, Germany
  • Year and Date: 2013-03-25
• [Presentation] Set Optimization with Set-Valued DC Functions (2012)
  • Author(s): D. Kuroiwa
  • Organizer: NAO-Asia 2012
  • Place of Presentation: くにびきメッセ(松江市)
  • Year and Date: 2012-09-05
• [Presentation] On DC set optimization problems (2012)
  • Author(s): D. Kuroiwa
  • Organizer: EURO 2012
  • Place of Presentation: Vilnius, Lithuania
  • Year and Date: 2012-07-10
• [Presentation] Set Optimization with Set-Valued DC Functions (2012)
  • Author(s): Kuroiwa, Daishi
  • Organizer: NAO-Asia 2012
  • Place of Presentation: くにびきメッセ（松江市）
  • Invited
• [Presentation] 非線形最適化と制約想定について (2011)
  • Author(s): 黒岩大史
  • Organizer: 研究会「最適化の理論と応用」
  • Place of Presentation: 新潟大学(新潟)
  • Year and Date: 2011-12-21
• [Presentation] 非線形最適化と制約想定について (2011)
  • Author(s): 黒岩大史
  • Organizer: 研究会「最適化の理論と応用」
  • Place of Presentation: 新潟大学
  • Year and Date: 2011-12-21
• [Presentation] Set Optimization with DC objective function (2011)
  • Author(s): Daishi Kuroiwa
  • Organizer: International Conference on Nonlinear Analysis and Convex Analysis
  • Place of Presentation: Pukyong National University(韓国・釜山)
  • Year and Date: 2011-08-04
• [Presentation] The BCQ for nonlinear programming problems (2011)
  • Author(s): Daishi Kuroiwa
  • Organizer: Workshop on analysis and optimization
  • Place of Presentation: Chung Li, Taiwan
  • Year and Date: 2011-03-30
• [Presentation] The BCQ for nonlinear programming problems (2011)
  • Author(s): Daishi Kuroiwa
  • Organizer: Workshop on analysis and optimization
  • Place of Presentation: Chung Li, Taiwan(招待講演)
  • Year and Date: 2011-03-30
• [Presentation] Set optimization and an embedding approach (2011)
  • Author(s): Daishi Kuroiwa
  • Organizer: International symposium on nonlinear analysisand convex analysis
  • Place of Presentation: Hualien, Taiwan
  • Year and Date: 2011-03-28
• [Presentation] Set optimization and an embedding approach (2011)
  • Author(s): Daishi Kuroiwa
  • Organizer: International symposium on nonlinear analysis and convex analysis
  • Place of Presentation: Hualien, Taiwan(招待講演)
  • Year and Date: 2011-03-28
• [Presentation] Set optimization and Lagrange duality (2010)
  • Author(s): Daishi Kuroiwa
  • Organizer: ICOTA 8
  • Place of Presentation: Shanghai, China
  • Year and Date: 2010-12-11
• [Presentation] Set optimization and duality results (2010)
  • Author(s): Daishi Kuroiwa
  • Organizer: NAO-Asia2010
  • Place of Presentation: Phuket, Thailand
  • Year and Date: 2010-09-10
• [Presentation] On constraint qualification for set programming problems (2010)
  • Author(s): D. Kuroiwa
  • Organizer: 研究集会「非線形解析学と凸解析学の研究」
  • Place of Presentation: 京都大学数理解析研究所(京都)
  • Year and Date: 2010-08-31
• [Presentation] On constraint qualification for set programming problems (2010)
  • Author(s): Daishi Kuroiwa
  • Organizer: 研究集会「非線形解析学と凸解析学の研究」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-08-31