Nonconvex and Nonsmooth Sparse Optimization via Adaptively Iterative Reweighted Methods

We propose a general formulation of nonconvex and nonsmooth sparse optimization problems with convex set constraint, which can take into account most existing types sparsity-inducing terms, bringing strong applicability to wide range applications. design algorithmic framework iteratively reweighted algorithms for solving the proposed problems, solves sequence weighted regularization adaptively updated weights. First-order optimality condition is derived global convergence results are provided under loose assumptions, making our theoretical practical tool analyzing family various algorithms. The effectiveness efficiency demonstrated in numerical experiments on problems.