2006 Fiscal Year Final Research Report Summary
Study on Nonlinear Scalarization Methods for Set-Valued Maps and its Applications into Mathematical Programming Problems and Statistical Science.
| Project/Area Number |
17540108
|
|---|
| 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 | Niigata University |
|---|
Principal Investigator |
TANAKA Tamaki Niigata University, Institute of Science and Technology, Professor, 自然科学系, 教授 (10207110)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
ISOGAI Eiichi Niigata University, Institute of Science and Technology, Professor, 自然科学系, 教授 (40108014)
YAMADA Syuuji Niigata University, Institute of Science and Technology, Associate Professor, 自然科学系, 助教授 (80331544)
TANINO Tetsuzo Osaka University, Graduate School of Engineering, Professor, 大学院工学研究科, 教授 (50125605)
|
|---|
| Project Period (FY) |
2005 – 2006
|
| Keywords | vector optimization / nonlinear scalarization / set-valued map / vector-valued function / Caristi's fixed point theorem / saddle point / global optimization |
|---|
| Research Abstract |
In this research, we have studied several kinds of themes on vector optimization and nonlinear scalarization methods for set-valued maps analytically and broadly, and then we have applied to multi-dimensional data in a statistical science.
1.We presented six papers for fundamental researches on nonlinear scalarizing functions and its applied researches into game theory at the Fourth International Conferences on Nonlinear Analysis and Convex Analysis (NACA2005,Okinawa). The papers have been published in the (refereed) proceedings,2006. They are related to (i)Caristi's fixed point theorems for vector-valued functions, (ii)existence results of cone saddle-points for vector-valued functions by using the Fan-KKM lemma, (iii)optimality conditions for efficient solutions in set-valued vector optimization problems.
2.As an application in mathematical programming, we researched outer approximation methods for global optimization problems with Associate Professor Yamada and Professor Tanino (Osaka
… More
University) jointly. Professor Tanino obtained chaos generator based on the affine scaling method for global optimization problems, and its paper was published.
3.As an application into multi-dimensional data in a statistical science, Professor Isogai considered presumption problems of arbitrary and possibly non-smooth densities.
4.In abroad, we presented our results in the 8-th International Symposium on Generalized Convexity/Monotonicity (Varese, Italy), the 3rd Sino-Japanese Optimization Meeting in the e-Business Era (SJOM 2005)(Singapore). We delivered invited talks at Chung Yuan Christian University, National Sun Yat-sen University, National Tsing-Hua University, Aletheia University, National Cheng Kung University, Changhua University of Education in Taiwan.
5.In Japan, we presented our results in RIMS Symposium on Nonlinear Analysis and Convex Analysis (Kyoto University), the symposium on developments of mathematical decision and its application (Department of Economics at Nagasaki University), the symposium on decision to mathematical model and its application (Department of Science at Kochi University). Less
|
Research Products
(22 results)
