| This paper studies the theory and algorithm of a class of sparse optimal folding concavity penalty.The folded concave continuous penalty is used to continuously approximate the L0 norm,that is,the objective function is composed of a non-smooth convex loss function and a folded concave penalty function,and a continuous relaxation model is obtained.、The equivalence relation between the solutions of these two problems(L0 problem and relaxation problem)is studied.Firstly,we focus on the properties of the relaxation model and analyze the equivalence between the cardinal penalty problem and the relaxation problem un-der the theoretical properties of the solution.Secondly,it is proved that these two problems have the same global optimal solution and optimal value under certain conditions.Finally,it is proved that the local optimal solution of the relaxation model is the local optimal solution of the cardinal penalty problem,and the relaxation model is equal to the optimal value of the cardinal penalty problem at the local minimum point.In this paper,the algorithm of smoothing acceleration proximal gradient is adopted to solve the relaxation problem.The main steps are to combine the original algorithm of smooth-ing acceleration proximal gradient with smoothing method,smoothing the non-smooth loss function,introducing an auxiliary sequence,and proving the convergence of the algorithm by proving the convergence of the auxiliary sequenceFinally,a numerical experiment is carried out on the least squares regression problem,including the simulation of the least squares random problem,the recovery of sparse signals and the comparison with the smoothing proximal gradient algorithm.Secondly,a numerical experiment is carried out on the censored regression models to illustrate the effectiveness of the algorithm... |
