Analytical Study on Vector Optimization and its Applications into Mathematical Programming Problems

向量优化及其在数学规划问题中的应用分析研究

• 批准号: 13640097
• 负责人: TANAKA Tamaki
• 金额: $ 2.43万
• 依托单位: NIIGATA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640097/
• 关键词: vector Optimization; minimax theorem; vector-valued function; set-valued map; cone-convexity; semicontinuity; game theory; multicriteria problems; Vector Optimization; minimax theorem; vector-valued function; set-valued map; cone-convexity; s

In this research, we have studied several kinds of themes on vector optimization analytically and broadly and then we got some results on saddle point's existence, vector equilibrium problem, convexity and semicontinuity for set-valued maps under systematic research and investigation. Moreover, we have studied on efficient solutions of multicriteria location problems. The main results and presentations are as follows.1.We presented our results on characterization of efficient solutions and existence of cone saddle points at The Second and Third International Conferences on Nonlinear Analysis and Convex Analysis(NACA2001,NACA2003), held at Hirosaki University and Tokyo Institute of Technology, August 2001 and August 2003, respectively. We delivered invited talks on multicriteria minimax inequality which is fundamental for cone saddle point of vector-valued function at NACA2003 and Workshop on Nonlinear Analysis & Convex Analysis, November 2003. Moreover, we organized the Fifth International Conference on Multi-Objective Programming and Goal Programming : Theory & Applications(MOPGP'02) at Nara, June 2002, and we discussed several problems and topics in this meeting.2.We presented our results on several inherited properties of scalarizing functions from convexity and semicontinuity of set-valued maps at NACA2001, MOPGP'02, and NACA2003. These results were presented in RIMS Symposium on Nonlinear Analysis and Convex Analysis.3.We presented our results on multicriteria game at NACA2001,MOPGP'02, and NACA2003.4.We presented our results on multicriteria location problems at NACA2001 and NACA2003. These results were presented in RIMS Symposium on Nonlinear Analysis and Convex Analysis. We also presented them at the research group of "decision and OR" of the Operations Research Society of Japan, held at Fukui University of Technology.

在这项研究中，我们对向量优化的几种主题进行了分析和广泛的研究，并在系统的研究和探索下，得到了关于集值映射的鞍点的存在性、向量平衡问题、凸性和半连续性的一些结果。此外，我们还研究了多目标选址问题的有效解。主要结果和成果如下：1.我们分别于2001年8月和2003年8月在广崎大学和东京工业大学举行的第二届和第三届国际非线性分析和凸分析会议(NACA2001，NACA2003)上介绍了我们关于有效解的刻画和锥鞍点的存在性的结果。我们在2003年NACA2003和2003年11月的非线性分析和凸分析研讨会上发表了关于多准则极大极小不等式的特邀演讲，这是向量值函数的锥鞍点的基础。此外，我们于2002年6月在奈良举办了第五届国际多目标规划与目标规划：理论与应用会议(MOPGP‘02)，并讨论了一些问题和主题。2.我们在NACA2001、MOPGP’02和NACA2003会议上介绍了集值映射凸性和半连续性中标化函数的几个继承性质。这些结果发表在RIMS非线性分析和凸分析研讨会上。3.我们在NACA2001、MOPGP‘02和NACA2003.4上介绍了我们关于多目标对策的结果。这些结果发表在RIMS非线性分析和凸分析研讨会上。我们还在福井工业大学举行的日本运筹学学会“Decision And OR”研究组上展示了它们。

项目成果

金 正道: "ファジィ多目的配置問題について"RIMS Kokyuroku 京都大学数理解析研究所講究録. Vol.1365(印刷中). (2004)

Kim Jeong-do：“关于模糊多目标放置问题”RIMS Kokyuroku 京都大学数学科学研究所讲座记录第 1365 卷（出版中）。

Shogo Nishizawa: "On inherited properties of set-valued maps"Proceedings of the Second International Conference on Nonlinear Analysis and Convex Analysis. 341-350 (2003)

Shogo Nishizawa：“论集值映射的继承性质”第二届非线性分析和凸分析国际会议论文集。

Kenji Kimura: "Some Types of Existence Theorems for Cone Saddle Points"RIMS Kokyuroku 京都大学数理解析研究所講究録. Vol.1298. 141-150 (2002)

Kenji Kimura：“锥鞍点的某些类型的存在定理”RIMS Kokyuroku 京都大学数学科学研究所 Kokyuroku 第 1298 卷（2002 年）。

B.J.ZHANG, S.NISHIZAWA, T.TANAKA: "On Inherited Properties and Scalarization Algorithms for Set-Valued Maps"RIMS Kokyuroku. 1246. 148-155 (2002)

B.J.ZHANG、S.NISHIZAWA、T.TANAKA：“关于集值映射的继承属性和标量化算法”RIMS Kokyuroku。

Masamichi Kon: "Efficient solutions of multicriteria location problems with the polyhedral gauge"Scientiae Mathematicae Japonicae. Vol.57. 177-185 (2003)

Masamichi Kon：“多面体规范多标准定位问题的有效解决方案”Scientiae Mathematicae Japonicae。