Inertial Alternating Direction Method Of Multipliers For A Class Of Nonconvex Optimization Problems With Linear Constraints

The alternating direction method of multipliers(ADMM)is an effective algorithm for solving separable optimization problems.It has been quite mature in solving convex optimization problems,but most practical models are nonconvex optimization problems,solving nonconvex optimization problems by ADMM is still under exploration.In addition,the combination of inertial technique and many first-order algorithm can effectively improve the numerical performance of the algorithm,which has been well proved.Therefore,in this paper,considering solving a class of nonconvex optimization problems,a new improved algorithm is proposed by combining the alternating direction method of multipliers with inertial technique.First of all,by combining inertial technique with proximal alternating direction method of multipliers,we propose inertial proximal alternating direction method of multipliers(i PADMM)to solving nonconvex optimization problems.We analyze the global convergence and strong convergence of the algorithm,which is applied to solve the problem of signal recovery and image reconstruction.What's more,in view of the above problem,we propose the inertial proximal symmetric alternating direction method of multipliers(ips-ADMM)by combining inertial technique with proximal symmetric alternating direction method of multipliers.Under the condition that the associated objective function satisfies Kurdyka-(?)ojasiewicz property,we analyze the strong convergence of the algorithm,which is applied to solve the problem of SCAD penalty problem.