表題番号：2023C-083
日付：2024/04/03
研究課題大規模緩和最適輸送問題における輸送行列の高効率スクリーニング手法の研究
| 研究者所属（当時） | 資格 | 氏名 | |
|---|---|---|---|
| （代表者） | 理工学術院 基幹理工学部 | 教授 | 笠井 裕之 |
- 研究成果概要
- We introduce a framework that utilizes the Safe Screening technique to accelerate the optimization process of the Unbalanced Optimal Transport (UOT) problem by proactively identifying and eliminating zero elements in the sparse solutions. We demonstrate the feasibility of applying Safe Screening to the UOT problem with ℓ2-penalty and KL-penalty by analyzing the solution’s bounds and considering the local strong convexity of the dual problem. Considering the specific structural characteristics of the UOT in comparison to general Lasso problems on the index matrix, we propose a novel approximate projection, an elliptical safe region construction, and a two-hyperplane relaxation method. These enhancements significantly improve the screening efficiency for the UOT’s without altering the algorithm’s complexity.