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2011 Fiscal Year Final Research Report

Study on Nonlinear Scalarization Methods for Set-Valued Maps and its Applications into Mathematical Programming

Research Project

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Project/Area Number 21540121
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionNiigata University

Principal Investigator

TANAKA Tamaki  新潟大学, 自然科学系, 教授 (10207110)

Co-Investigator(Kenkyū-buntansha) ISOGAI Eiichi  新潟大学, 自然科学系, 教授 (40108014)
YAMADA Syuuji  新潟大学, 自然科学系, 准教授 (80331544)
Co-Investigator(Renkei-kenkyūsha) TANINO Tetsuzo  大阪大学, 大学院・工学研究科, 教授 (50125605)
KUROIWA Daishi  島根大学, 総合理工学部, 教授 (40284020)
Project Period (FY) 2009 – 2011
Keywords集合値計画 / 非線形スカラー化関数 / 均衡問題 / 集合値最適化 / ベクトル最適化 / 凸解析学 / 数理計画問題 / 大域的最適化
Research Abstract

In this study, we give theoretical analysis on nonlinear scalarization methods for sets, which has been introduced in the previous study(research 21540121 supported by Grant-in-Aid for Scientific Research(C)), and we research algorithm development for its numerical calculations and its applications. That is to say we derive several mathematical properties related to certain inequalities for set-valued maps by the help of classical theory through the use of the invariant property of some scalarization methods for set-relationship.

  • Research Products

    (53 results)

All 2012 2011 2010 2009 Other

All Journal Article (18 results) (of which Peer Reviewed: 18 results) Presentation (35 results)

  • [Journal Article] Optimality condition for vector-valued DC programming problems2012

    • Author(s)
      M. Hojo and T. Tanaka
    • Journal Title

      J. Nonlinear Convex Anal.

      Volume: 13(1) Pages: 57-64

    • Peer Reviewed
  • [Journal Article] Improvements by analyzing the efficient frontier in DEA2012

    • Author(s)
      S. Washio, S. Yamada, T. Tanaka, and T. Tanino
    • Journal Title

      European Journal of Operational Research

      Volume: 217(1) Pages: 173-184

    • DOI

      DOI:10.1016/j.ejor.2011.09.002

    • Peer Reviewed
  • [Journal Article] On Regularity for Non-Additive Measure2011

    • Author(s)
      T. Watanabe and T. Tanaka
    • Journal Title

      Advances in Intelligent and Soft Computing

      Pages: 69-75

    • DOI

      DOI:10.1007/978-3-642-22833-9_8

    • Peer Reviewed
  • [Journal Article] On Lusin's Theorem for Non-Additive Measure2011

    • Author(s)
      T. Tanaka and T. Watanabe
    • Journal Title

      Advances in Intelligent and Soft Computing

      Pages: 85-92

    • DOI

      DOI:10.1007/978-3-642-22833-9_10

    • Peer Reviewed
  • [Journal Article] Outer approximation method incorporating the Ferrari's method for solving a quadratic dc programming problem2011

    • Author(s)
      S. Yamada, T. Tanaka, and T. Tanino
    • Journal Title

      J. Nonlinear Convex Anal.

      Volume: 12(1) Pages: 17-27

    • Peer Reviewed
  • [Journal Article] Improvement indices keeping the feasibility in deta envelopment analysis2011

    • Author(s)
      S. Washio, S. Yamada, T. Tanaka, and T. Tanino
    • Journal Title

      J. Nonlinear Convex Anal.

      Volume: 12(1) Pages: 29-48

    • Peer Reviewed
  • [Journal Article] Dual and bidual problems for a Lipschitz optimization problem based on quasi-conjugation2011

    • Author(s)
      S. Yamada, T. Tanaka, and T. Tanino
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 378 Pages: 198-212

    • Peer Reviewed
  • [Journal Article] Cone-semicontinuity of set-valued maps by analogy with real-valued semicontinuity2010

    • Author(s)
      Y. Sonda, I. Kuwano, and T. Tanaka
    • Journal Title

      Nihonkai Math. J

      Volume: 21(2) Pages: 91-103

    • Peer Reviewed
  • [Journal Article] Unified scalarization for sets and set-valued Ky Fan minimax inequalities2010

    • Author(s)
      I. Kuwano, T. Tanaka, and S. Yamada
    • Journal Title

      J. Nonlinear Convex Anal.

      Volume: 11(3) Pages: 513-525

    • Peer Reviewed
  • [Journal Article] On generalizing Cammaroto-Chinni's theorem2010

    • Author(s)
      Y. Araya and T. Tanaka
    • Journal Title

      Nonlinear Analysis and Convex Analysis

      Pages: 29-35

    • Peer Reviewed
  • [Journal Article] On saddle-point problems for set-valued functions2010

    • Author(s)
      K. Kimura and T. Tanaka
    • Journal Title

      Nonlinear Analysis and Convex Analysis

      Pages: 115-124

    • Peer Reviewed
  • [Journal Article] Inherited properties of nonlinear scalarizing functions for set-valued maps2010

    • Author(s)
      I. Kuwano, T. Tanaka, and S. Yamada
    • Journal Title

      Nonlinear Analysis and Convex Analysis

      Pages: 161-177

    • Peer Reviewed
  • [Journal Article] Outer approximation methods incorporating Lipschitz optimization techniques for solving a DC programming problem2010

    • Author(s)
      S. Yamada, T. Tanaka, and T. Tanino
    • Journal Title

      Nonlinear Analysis and Convex Analysis

      Pages: 417-432

    • Peer Reviewed
  • [Journal Article] Outer approximation method incorporating a quadratic approximation for a dc programming problem2010

    • Author(s)
      S. Yamada, T. Tanaka, and T. Tanino
    • Journal Title

      Journal of Optimization Theory and Applications

      Volume: 144(1) Pages: 156-183

    • Peer Reviewed
  • [Journal Article] Sequential estimation of a linear function of location parameters of two negative exponential distributions2010

    • Author(s)
      E. Isogai and A. Futschik
    • Journal Title

      Journal of Statistical Planning and Inference

      Volume: 140(9) Pages: 2416-2424

    • Peer Reviewed
  • [Journal Article] Characterization of nonlinear scalarizing functions for set-valued maps2009

    • Author(s)
      I. Kuwano, T. Tanaka, and S. Yamada
    • Journal Title

      Proceedings of Asian Conference on Nonlinear Analysis and Optimization

      Pages: 193-204

    • Peer Reviewed
  • [Journal Article] A dual problem for a Lipschitz optimization problem2009

    • Author(s)
      S. Yamada, T. Tanaka, and T. Tanino
    • Journal Title

      Proceedings of Asian Conference on Nonlinear Analysis and Optimization

      Pages: 349-359

    • Peer Reviewed
  • [Journal Article] Continuity of cone-convex functions

    • Author(s)
      I. Kuwano and T. Tanaka
    • Journal Title

      Optimization Letters

      Volume: (to appear)

    • DOI

      DOI:10.1007/s11590-011-0381-4

    • Peer Reviewed
  • [Presentation] 3規準二人ゼロ和行列ゲームに対する行列の分類2011

    • Author(s)
      樋口政和
    • Organizer
      「非線形解析学と凸解析学の研究」研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-08-31
  • [Presentation] ベクトル空間とChain完備な半順序ベクトル空間の直積における分離定理について2011

    • Author(s)
      渡辺俊一
    • Organizer
      「非線形解析学と凸解析学の研究」研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-08-31
  • [Presentation] 混合整数計画問題に対する最適化について2011

    • Author(s)
      山田修司
    • Organizer
      「非線形解析学と凸解析学の研究」研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-08-31
  • [Presentation] スカラー化を用いた集合値写像のEkelandの定理2011

    • Author(s)
      久保貴大
    • Organizer
      「非線形解析学と凸解析学の研究」研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-08-31
  • [Presentation] 集合値写像に対するミニマックス定理2011

    • Author(s)
      桑野一成
    • Organizer
      「非線形解析学と凸解析学の研究」研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-08-31
  • [Presentation] ベクトル値DC計画問題に対する最適条件について2011

    • Author(s)
      北條真弓
    • Organizer
      「非線形解析学と凸解析学の研究」研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-08-31
  • [Presentation] Some minimax theorems for set-valued maps2011

    • Author(s)
      Tamaki Tanaka
    • Organizer
      The Seventh International Conference on Nonlinear Analysis and Convex Analysis(非線形解析学と凸解析学に関する第7回国際会議, NACA2011)
    • Place of Presentation
      韓国釜山市,国立釜慶大学校
    • Year and Date
      2011-08-04
  • [Presentation] Saddle point theorems for set-valued maps2011

    • Author(s)
      Issei Kuwano
    • Organizer
      The Seventh International Conference on Nonlinear Analysis and Convex Analysis(非線形解析学と凸解析学に関する第7回国際会議, NACA2011)
    • Place of Presentation
      韓国釜山市,国立釜慶大学校
    • Year and Date
      2011-08-04
  • [Presentation] Ekeland's variational principle for set-valued maps via scalarization2011

    • Author(s)
      Takahiro Kubo
    • Organizer
      The Seventh International Conference on Nonlinear Analysis and Convex Analysis(非線形解析学と凸解析学に関する第7回国際会議, NACA2011)
    • Place of Presentation
      韓国釜山市,国立釜慶大学校
    • Year and Date
      2011-08-04
  • [Presentation] Duality for Lipschitz optimization over the weakly efficient set based on quasi-conjugation2011

    • Author(s)
      Syuuji Yamada
    • Organizer
      The Seventh International Conference on Nonlinear Analysis and Convex Analysis(非線形解析学と凸解析学に関する第7回国際会議, NACA2011)
    • Place of Presentation
      韓国釜山市,国立釜慶大学校
    • Year and Date
      2011-08-02
  • [Presentation] Successive approximation algorithms for solving a canonical DC programming problem2011

    • Author(s)
      Syuuji Yamada
    • Organizer
      the 19th Triennial Conference of the International Federation of Operational Research Societies
    • Place of Presentation
      Melbourne Convention and Exhibition Centre, Melbourne, Australia
    • Year and Date
      2011-07-10
  • [Presentation] Expansion of the cross efficiency evaluation in DEA2010

    • Author(s)
      Satoshi Washio
    • Organizer
      The 8th International Conference on Optimization : Techniques and Applications(最適化の技術と応用に関する第8回国際会議, ICOTA8)
    • Place of Presentation
      中華人民共和国,上海市,復旦大学
    • Year and Date
      2010-12-13
  • [Presentation] Successive search methods for a canonical dc programming problem2010

    • Author(s)
      Syuuji Yamada
    • Organizer
      The 8th International Conference on Optimization : Techniques and Applications(最適化の技術と応用に関する第8回国際会議, ICOTA8)
    • Place of Presentation
      中華人民共和国,上海市,復旦大学
    • Year and Date
      2010-12-12
  • [Presentation] Inherited properties of nonlinear scalarizing functions for set-valued maps2010

    • Author(s)
      Tamaki Tanaka
    • Organizer
      The 8th International Conference on Optimization : Techniques and Applications(最適化の技術と応用に関する第8回国際会議, ICOTA8)
    • Place of Presentation
      中華人民共和国,上海市,復旦大学
    • Year and Date
      2010-12-11
  • [Presentation] Some minimax theorems for set-valued maps2010

    • Author(s)
      Issei Kuwano
    • Organizer
      The 8th International Conference on Optimization : Techniques and Applications(最適化の技術と応用に関する第8回国際会議, ICOTA8)
    • Place of Presentation
      中華人民共和国,上海市,復旦大学
    • Year and Date
      2010-12-11
  • [Presentation] DEAにおいて加重和を用いた全順序評価2010

    • Author(s)
      鷲尾哲
    • Organizer
      2010年日本オペレーションズ・リサーチ学会秋季研究発表会
    • Place of Presentation
      福島県福島市,コラッセ福島
    • Year and Date
      2010-09-17
  • [Presentation] Generalized Fan's inequalities for se-valued maps via scalarization2010

    • Author(s)
      Issei Kuwano
    • Organizer
      The Second Asian Conference on Nonlinear Analysis and Optimization(第2回非線形解析学と最適化に関するアジア会議, NAO-Asia2010)
    • Place of Presentation
      タイ・プーケット,ロイヤルパラダイスホテル
    • Year and Date
      2010-09-11
  • [Presentation] A global optimization method searching a feasible solution in two-dimensional subspace for solving a dc programming problem2010

    • Author(s)
      Syuuji Yamada
    • Organizer
      The Second Asian Conference on Nonlinear Analysis and Optimization(第2回非線形解析学と最適化に関するアジア会議, NAO-Asia2010)
    • Place of Presentation
      タイ・プーケット,ロイヤルパラダイスホテル
    • Year and Date
      2010-09-11
  • [Presentation] Nonlinear scalarizing functions for set-valued maps and its applications2010

    • Author(s)
      Tamaki Tanaka
    • Organizer
      The Second Asian Conference on Nonlinear Analysis and Optimization(第2回非線形解析学と最適化に関するアジア会議, NAO-Asia2010)
    • Place of Presentation
      タイ・プーケット,ロイヤルパラダイスホテル
    • Year and Date
      2010-09-09
  • [Presentation] Pareto-efficient target by obtaining the facets of the efficient frontier in DEA2010

    • Author(s)
      Satoshi Washio
    • Organizer
      The Second Asian Conference on Nonlinear Analysis and Optimization(第2回非線形解析学と最適化に関するアジア会議, NAO-Asia2010)
    • Place of Presentation
      タイ・プーケット,ロイヤルパラダイスホテル
    • Year and Date
      2010-09-09
  • [Presentation] 半順序ベクトル空間におけるHahn Banach定理について2010

    • Author(s)
      渡辺俊一
    • Organizer
      「非線形解析学と凸解析学の研究」研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-09-01
  • [Presentation] 非線形スカラー化手法を用いた集合値写像の鞍点の存在定理2010

    • Author(s)
      Issei Kuwano
    • Organizer
      「非線形解析学と凸解析学の研究」研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-09-01
  • [Presentation] 閉凸錐で定義された弱有効解集合上での最適化に対する内部近似法2010

    • Author(s)
      安藤圭太
    • Organizer
      「非線形解析学と凸解析学の研究」研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-09-01
  • [Presentation] DC計画問題に対する内部近似法2010

    • Author(s)
      山田修司
    • Organizer
      第54回システム制御情報学会研究発表講演会
    • Place of Presentation
      京都府京都市,京都リサーチパーク
    • Year and Date
      2010-05-21
  • [Presentation] Inherited properties of nonlinear scalarizing functions for set-valued maps2010

    • Author(s)
      Tamaki Tanaka
    • Organizer
      International Symposium2010 : Nonlinear Analysis and Optimization
    • Place of Presentation
      韓国釜山市,国立釜慶大学校
    • Year and Date
      2010-02-05
  • [Presentation] On nonlinear scalarizing functions for set-valued maps2009

    • Author(s)
      Tamaki Tanaka
    • Organizer
      Abstract Harmonic Analysis 2009
    • Place of Presentation
      台湾高雄市,国立中山大学
    • Year and Date
      2009-12-19
  • [Presentation] DEAにおける実現可能性を考慮した効率測定2009

    • Author(s)
      鷲尾哲
    • Organizer
      第52回自動制御連合講演会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-11-22
  • [Presentation] ベクトル空間における集合のスカラー化数値計算法について2009

    • Author(s)
      田中環
    • Organizer
      第52回自動制御連合講演会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-11-21
  • [Presentation] リプシッツ最適化問題に対する頂点間の連結関係を用いた内部近似法2009

    • Author(s)
      山田修司
    • Organizer
      第52回自動制御連合講演会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-11-21
  • [Presentation] ベクトル空間における集合のスカラー化数値計算法について2009

    • Author(s)
      田中環
    • Organizer
      日本オペレーションズ・リサーチ学会秋季研究発表会
    • Place of Presentation
      長崎大学
    • Year and Date
      2009-09-10
  • [Presentation] リプシッツ最適化問題に対する切除平面法を導入した内部近似法2009

    • Author(s)
      山田修司
    • Organizer
      日本オペレーションズ・リサーチ学会秋季研究発表会
    • Place of Presentation
      長崎大学
    • Year and Date
      2009-09-10
  • [Presentation] DEAにおいて実現可能性を考慮した改善指標2009

    • Author(s)
      鷲尾哲
    • Organizer
      「非線形解析学と凸解析学の研究」研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-09-02
  • [Presentation] 集合に対する統一的なスカラー化関数の性質といくつかの例2009

    • Author(s)
      孫田祐哉
    • Organizer
      「非線形解析学と凸解析学の研究」研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-09-02
  • [Presentation] Unified scalarization for sets in set-valued optimization2009

    • Author(s)
      桑野一成
    • Organizer
      「非線形解析学と凸解析学の研究」研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-09-02
  • [Presentation] Inherited properties of nonlinear scalarizing functions for set-valued maps2009

    • Author(s)
      Tamaki Tanaka
    • Organizer
      The 9th International Conference on Fixed Point Theory and Its Applications
    • Place of Presentation
      台湾彰化市,国立彰化師範大学
    • Year and Date
      2009-07-18

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Published: 2013-07-31  

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