A Projection Proximal-Point Algorithm for 1 Minimization

作者：Lorenz Dirk A^*

来源：Numerical Functional Analysis and Optimization, 2010, 31(2): 172-190.

DOI：10.1080/01630560903381712

• Proximal point algorithm
• Sparse reconstruction
• Sparsity constraint

The problem of the minimization of least squares functionals with 1 penalties is considered in an infinite dimensional Hilbert space setting. Though there are several algorithms available in the finite dimensional setting there are only a few of them that come with a proper convergence analysis in the infinite dimensional setting. In this work we provide an algorithm from a class that has not been considered for 1 minimization before, namely, a proximal-point method in combination with a projection step. We show that this idea gives a simple and easy-to-implement algorithm. We present experiments that indicate that the algorithm may perform better than other algorithms if we employ them without any special tricks. Hence, we may conclude that the projection proximal-point idea is a promising idea in the context of 1 minimization.

• 出版日期2010