Accelerated first-order continuous-time algorithm for solving convex-concave bilinear saddle point problem

First-order methods have simple structures and are of great importance to big data problems because first-order methods are easy to implement in a distributed or parallel way. However, in the worst cases, first-order methods often converge at a rate O(1/t), which is slow. This paper considers a class of convex-concave bilinear saddle point problems and proposes an accelerated first-order continuous-time algorithm. We design the accelerated algorithm by using both increasing and decreasing damping coefficients in the saddle point dynamics. If parameters of the proposed algorithm are proper, the algorithm owns O(1/t²) convergence without any strict or strong convexity requirement. Finally, we apply the algorithm to numerical examples to show the superior performance of the proposed algorithm over existing ones.