GENERALIZED PROXIMAL ITERATIVELY REWEIGHTED ℓ₁ ALGORITHM WITH CO-COERCIVENESS FOR NONSMOOTH AND NONCONVEX MINIMIZATION PROBLEM

GENERALIZED PROXIMAL ITERATIVELY REWEIGHTED ℓ₁ ALGORITHM WITH CO-COERCIVENESS FOR NONSMOOTH AND NONCONVEX MINIMIZATION PROBLEM

The nonconvex and nonsmooth optimization problem has been widely applicable in image processing and machine learning. In this paper, we propose an extension of the proximal it-eratively reweighted ℓ1 algorithm for nonconvex and nonsmooth minmization problem. We assume the co-coerciveness of a term of objective function instead of Lipschitz gradient condition, which is generalized property of Lipschitz continuity. We prove the global convergence of the proposed algorithm. Numerical results show that the proposed algorithm converges faster than original proximal iteratively reweighed algorithm and existing algorithms