Abstract
In this paper, we construct a variant of the second accelerated proximal gradient method introduced by Nesterov (Introductory lectures on convex optimization, Kluwer Academic Publisher, Dordrecht, 2004) and Auslender and Teboulle (SIAM J Optim 16:697–725, 2006) [and named by Tseng (Math Program 125:263–295, 2010)] for solving the minimization of DC functions (difference of two convex functions). Under some suitable assumptions such as level boundedness, Kurdyka–Łojasiewicz property, and locally Lipschitz differentiability, we prove that the sequence generated by our algorithm locally linearly converges to some stationary point of the given DC function. Numerical results show that our method performs well and fast, comparing to some other often used algorithms.
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