On an iteratively reweighted linesearch based algorithm for nonconvex composite optimization

Proximal Iteratively Reweighted Algorithm with Multiple Splitting for Nonconvex Sparsity Optimization

This paper proposes the Proximal Iteratively REweighted (PIRE) algorithm for solving a general problem, which involves a large body of nonconvex sparse and structured sparse related problems. Comparing with previous iterative solvers for nonconvex sparse problem, PIRE is much more general and efficient. The computational cost of PIRE in each iteration is usually as low as the state-of-the-art c...

On Iteratively Reweighted Algorithms for Nonsmooth Nonconvex Optimization in Computer Vision

Natural image statistics indicate that we should use non-convex norms for most regularization tasks in image processing and computer vision. Still, they are rarely used in practice due to the challenge of optimization. Recently, iteratively reweighed `1 minimization (IRL1) has been proposed as a way to tackle a class of non-convex functions by solving a sequence of convex `2-`1 problems. We ext...

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients

an effective optimization algorithm for locally nonconvex lipschitz functions based on mollifier subgradients

Iteratively Reweighted $\ell_1$ Approaches to Sparse Composite Regularization

Motivated by the observation that a given signal x admits sparse representations in multiple dictionaries Ψd but with varying levels of sparsity across dictionaries, we propose two new algorithms for the reconstruction of (approximately) sparse signals from noisy linear measurements. Our first algorithm, Co-L1, extends the well-known lasso algorithm from the L1 regularizer ‖Ψx‖1 to composite re...