论文标题
基于双密度的重新加权$ \ ell_ {1} $ - $ \ ell_ {0} $的算法 - 最小化问题
Dual-density-based reweighted $\ell_{1}$-algorithms for a class of $\ell_{0}$-minimization problems
论文作者
论文摘要
稀疏性的优化问题在许多科学和工程领域（例如压缩传感，图像处理，统计学习和数据稀疏近似）出现。在本文中，我们研究了基于双密度的重新加权$ \ ell_ {1} $ - 算法 - $ \ ell_ {0} $ - 最小化模型，可用于建模各种实际问题。这类算法基于对基础$ \ ell_ {0} $的重新印度的某些凸放松 - 最小化模型。这样的重新重新制作是一个特殊的双重优化问题，从理论上讲，在严格互补性的假设下，在基本的$ \ ell_ {0} $ - 最小化问题上等同于最小化问题。讨论了这些算法的一些基本特性，并进行了数值实验以证明所提出的算法的效率。本文也进行了比较所提出的方法的数值表现和经典重新持续的$ \ ell_1 $ -1-烯烃的比较。
The optimization problem with sparsity arises in many areas of science and engineering such as compressed sensing, image processing, statistical learning and data sparse approximation. In this paper, we study the dual-density-based reweighted $\ell_{1}$-algorithms for a class of $\ell_{0}$-minimization models which can be used to model a wide range of practical problems. This class of algorithms is based on certain convex relaxations of the reformulation of the underlying $\ell_{0}$-minimization model. Such a reformulation is a special bilevel optimization problem which, in theory, is equivalent to the underlying $\ell_{0}$-minimization problem under the assumption of strict complementarity. Some basic properties of these algorithms are discussed, and numerical experiments have been carried out to demonstrate the efficiency of the proposed algorithms. Comparison of numerical performances of the proposed methods and the classic reweighted $\ell_1$-algorithms has also been made in this paper.
