Accelerated Algorithm For Solving Non-smooth DC Programs

Many real-world applications can be described as the nonconvex and nonsmooth problems.Compared with convex optimization theory,there are not many effective methods to study non-convex optimization.One way to deal with the nonconvex problems is converting it into DC(Difference of Convex)programming.Since DCA(DC Algorithm)was introduced in 1986,many researchers have paid extensive attention to it and lots of variant of DCA have been proposed.The aspect considered in this paper is to accelerate the convergence of DCA.Based on the classical DCA,this paper proposes the inexact DCA.Under the assumption of Kurdyka-Lojasiewicz property,we prove the convergence and convergence rate of the sequence of iterations.Based on the proximal DCA,this paper proposes improved proximal DCA and improved proximal DCA with extrapolation.The both methods accelerate the convergence speed of DCA.The convergence and convergence rate of the sequence of iterations can be obtained under the assumption of Kurdyka-(?)ojasiewicz(K(?))property.Numerical experiments demonstrate the effectiveness and practicability of the proposed algorithms.