Xu, Jialiang (2019). Algorithms and stability analysis for optimization problems with sparsity. University of Birmingham. Ph.D.
|
Xu2019PhD.pdf
Text - Accepted Version Available under License All rights reserved. Download (1MB) | Preview |
Abstract
The optimization models with sparsity arise in many areas of science and engineering, such as compressive sensing, image processing, statistical learning and machine learning. In this thesis, we study a general 10-minimization model, which can be used to deal with many practical applications. Firstly, we show some theoretical properties of the solutions of this model. Then, two types of re-weighted 11-algorithms will be developed from both the perspectives of primal and dual spaces, respectively. The primal re-weighted 11-algorithms will be derived through the 1st-order approximation of the so-called merit functions for sparsity. The dual re-weighted 11-algorithms for the general 10-model will be developed based on the reformulation of the general 10-model as a certain bilevel programming problem under the assumption of strict complementarity. We conduct numerical experiments to demonstrate the efficiency of the primal and dual re-weighted 11-algorithms and compare with some existing algorithms. We also establish a general stability result for a class of 11-minimization approach which is broad enough to cover many important special cases. Unlike the existing stability results developed under the null space property and restricted isotonic property, we use a classic Hoffman's theorem to establish a restricted-weak-RSP-based stability result for this class of 11-minimization approach.
Type of Work: | Thesis (Doctorates > Ph.D.) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
Award Type: | Doctorates > Ph.D. | |||||||||
Supervisor(s): |
|
|||||||||
Licence: | All rights reserved | |||||||||
College/Faculty: | Colleges (2008 onwards) > College of Engineering & Physical Sciences | |||||||||
School or Department: | School of Mathematics | |||||||||
Funders: | None/not applicable | |||||||||
Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Computer software |
|||||||||
URI: | http://etheses.bham.ac.uk/id/eprint/9303 |
Actions
Request a Correction | |
View Item |
Downloads
Downloads per month over past year