A Convex-Nonconvex Framework for Enhancing Minimization Induced Penalties

Abstract

This paper presents a novel framework for nonconvex enhancement of minimization induced (MI) penalties while preserving the overall convexity of associated regularization models. MI penalties enable the adaptation to certain signal structures via minimization, but often underestimate significant components owing to convexity. To overcome this shortcoming, we design a generalized Moreau enhanced minimization induced (GME-MI) penalty by subtracting from the MI penalty its generalized Moreau envelope. While the proposed GME-MI penalty is nonconvex in general, we derive an overall convexity condition for the GME-MI regularized least-squares model. Moreover, we present a proximal splitting algorithm with guaranteed convergence to a globally optimal solution of the GME-MI model under the overall convexity condition. Numerical examples illustrate the effectiveness of the proposed framework.

References in corpus (16)

• Nearly unbiased variable selection under minimax concave penalty
• Sparse Regularization via Convex Analysis
• A Selective Review of Group Selection in High-Dimensional Models
• Group-Sparse Signal Denoising: Non-Convex Regularization, Convex Optimization
• Sparse Signal Estimation by Maximally Sparse Convex Optimization
• Compressed Sensing Recovery via Nonconvex Shrinkage Penalties
• A Majorize-Minimize subspace approach for l2-l0 image regularization
• Enhanced Low-Rank Matrix Approximation
• On the Convergence of the Iterative Shrinkage/Thresholding Algorithm With a Weakly Convex Penalty
• Linearly Involved Generalized Moreau Enhanced Models and Their Proximal Splitting Algorithm under Overall Convexity Condition
• A Class of Nonconvex Penalties Preserving Overall Convexity in Optimization-Based Mean Filtering
• Total Generalized Variation for Manifold-valued Data
• Infimal convolution of oscillation total generalized variation for the recovery of images with structured texture
• Linearly-involved Moreau-Enhanced-over-Subspace Model: Debiased Sparse Modeling and Stable Outlier-Robust Regression
• Convex Estimation of Sparse-Smooth Power Spectral Densities from Mixtures of Realizations with Application to Weather Radar
• A Convex-Nonconvex Strategy for Grouped Variable Selection