The Accelerated Proximal Algorithm For A Class Of DC Optimization Problems And Its Convergence Analysis

We consider a class of DC?difference-of-convex?optimization problems,with level-bounded objective function which can be represented by the sum of a smooth convex function with Lipschitz gradient,a proper closed convex function and a continuous concave function.In this thesis we modify the second APG?accelerated proximal gradient?method of the three methods proposed by Nesterov[36]?and named by Tseng[41]?for solving the minimization of DC optimization.Under a fairly general choice of the proximal parameters{₆)},we show that any cluster point of the sequence generated by our algorithm is a stationary point of the DC optimization problem.Moreover,we prove that the sequence generated by our algorithm is linearly locally convergence by some suitable assumptions.Numerical results show that our method has good performance.At last,we generalize the APGalgorithm to the GMAPGs algorithm to solve TV-image deblurring problems.