Using LASSO for formulating constraint of least-squares programming for solving one-norm equality constrained problem
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- 作者：Ya Li ; Bingo Wing-Kuen Ling ; Langxiong Xie…
- 关键词：One ; norm equality constrained optimization ; Least absolute shrinkage and selection operator optimization ; Iterative shrinkage algorithm ; Fast iterative shrinkage thresholding algorithm ; Least ; squares constrained optimization ; Nonconvex optimization
- 刊名：Signal, Image and Video Processing
- 出版年：2017
- 出版时间：January 2017
- 年：2017
- 卷：11
- 期：1
- 页码：179-186
- 全文大小：
- 刊物类别：Engineering
- 刊物主题：Signal,Image and Speech Processing; Image Processing and Computer Vision; Computer Imaging, Vision, Pattern Recognition and Graphics; Multimedia Information Systems;
- 出版者：Springer London
- ISSN：1863-1711
- 卷排序：11
文摘
The paper proposes an efficient method for solving a one- norm equality constrained optimization problem. In fact, this kind of optimization problems is nonconvex. First, the problem is formulated as the least absolute shrinkage and selection operator (LASSO) optimization problem. Then, it is solved by iterative shrinkage algorithms such as the fast iterative shrinkage thresholding algorithm. Next, the solution of the LASSO optimization problem is employed for formulating the constraint of the corresponding least-squares constrained optimization problem. The solution of the least-squares constrained optimization problem is taken as a near globally optimal solution of the one-norm equality constrained optimization problem. The main advantage of this proposed method is that a solution with both lower one-norm constraint error and two-norm reconstruction error can be obtained compared to those of the LASSO problem, while the required computational power is significantly reduced compared to the full search approach. Computer numerical simulation results are illustrated.