Sparse Optimization Problem with s-difference Regularization

Abstract

In this paper, a s-difference type regularization for sparse recovery problem is proposed, which is the difference of the normal penalty function R(x) and its corresponding struncated function R (xs). First, we show the equivalent conditions between the L0 constrained problem and the unconstrained s-difference penalty regularized problem. Next, we choose the forward-backward splitting (FBS) method to solve the nonconvex regularizes function and further derive some closed-form solutions for the proximal mapping of the s-difference regularization with some commonly used R(x), which makes the FBS easy and fast. We also show that any cluster point of the sequence generated by the proposed algorithm converges to a stationary point. Numerical experiments demonstrate the efficiency of the proposed s-difference regularization in comparison with some other existing penalty functions.

arXiv comment20 pages, 5 figures

References in corpus (8)

• Nearly unbiased variable selection under minimax concave penalty
• Sparse Regularization via Convex Analysis
• Image Compressive Sensing Recovery Using Adaptively Learned Sparsifying Basis via L0 Minimization
• Accelerating the DC algorithm for smooth functions
• Statistical estimation and testing via the sorted L1 norm
• Efficient DC Algorithm for Constrained Sparse Optimization
• Sequential Convex Programming Methods for A Class of Structured Nonlinear Programming
• An accelerated proximal iterative hard thresholding method for ${\ell }_0$ minimization