2013 Fiscal Year Final Research Report
The hierarchical optimization problem and its related topics
| Project/Area Number |
21300091
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Sensitivity informatics/Soft computing
|
|---|
| Research Institution | Tokyo Institute of Technology |
|---|
Principal Investigator |
ISAO Yamada 東京工業大学, 理工学研究科, 教授 (50230446)
|
|---|
| Project Period (FY) |
2009-04-01 – 2014-03-31
|
| Keywords | 階層構造を持つ最適化問題 / ハイブリッド最急降下法 / モローの正則化 / 疎情報適応学習アルゴリズム / テンソル補間アルゴリズム / 低階数最小分散擬似不偏法 / ランク選択問題 / 一般化固有値問題 |
|---|
| Research Abstract |
In this research project, we have tackled the hierarchical optimization problem and its related topics.In the 1st part,motivated by recent elegant characterizations of the solution sets of convex optimization problems as the fixed point sets of computable nonexpansive mappings, we present an algorithmic selection of an optimal point in the solution set of a convex optimization problem based on the hybrid steepest descent method and the Moreau regularization. In the process, we also developed proximal type algorithms for the sparsity aware adaptive learning problems, convex optimization algorithms for the tensor completion problems.In the 2nd part, we tackled mainly case studies of the hierarchical nonconvex optimization problems. These include, e.g., the optimal rank selection of the minimum-variance pseudo-unbiased reduced-rank estimator (MV-PURE) for ill-conditioned linear inverse problems. and the generalized eigenvalue problem for efficient adaptive subspace extraction.
|
