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This work presents a universal accelerated first-order primal-dual method foraffinely constrained convex optimization problems. It can handle both Lipschitzand H\"{o}lder gradients but does not need to know the smoothness level of theobjective function. In line search part, it uses dynamically decreasingparameters and produces approximate Lipschitz constant with moderate magnitude.In addition, based on a suitable discrete Lyapunov function and tight decayestimates of some differential/difference inequalities, a universal optimalmixed-type convergence rate is established. Some numerical tests are providedto confirm the efficiency of the proposed method.

A universal accelerated primal-dual method for convex optimization problems