An Alternating Direction Method Of Multipliers For (?)_p Quasi-norm Regularized Model

Sparse optimization problems are mathematical models describing variable selection,error correction,compressed sensing,cardinality constrained portfolio optimization prob-lems,etc.The(?)_pquasi-norm model has shown better performance in many applications.The(?)_pquasi-norm model is nonconvex and nonsmooth,and has been proved NP-hard.In this paper,by introducing auxiliary variables,the(?)_pquasi-norm regularized model is reconstructed into an optimization model with separable variables.An alternating direc-tion method of multipliers is designed to solve the problem.We analyze the convergence of the algorithm.The algorithm is applied to solve sparse optimization problems such as vector recovery and cardinality constrained portfolio problems.Computation results show the effectiveness of the algorithm.