Fast gradient methods for uniformly convex and weakly smooth problems

In this paper, acceleration of gradient methods for convex optimization problems with weak levels convexity and smoothness is considered. Starting from the universal fast method which was designed to be an optimal weakly smooth whose gradients are Hölder continuous, its momentum modified appropriately so that it can also accommodate uniformly problems. Different existing works, proposed in paper do not use restarting technique but momentums suitably reflect both uniform information target energy function. Both theoretical numerical results support superiority presented.