Self-adaptive ADMM for semi-strongly convex problems
- In this paper, we develop a self-adaptive ADMM that updates the penalty parame-
ter adaptively. When one part of the objective function is strongly convex i.e., the
problem is semi-strongly convex, our algorithm can update the penalty parameter
adaptively with guaranteed convergence. We establish various types of convergence
results including accelerated convergence rate of O(1/k2), linear convergence and
convergence of iteration points. This enhances various previous results because we
allow the penalty parameter to change adaptively. We also develop a partial proximal
point method with the subproblems being solved by our adaptive ADMM. This enables
us to solve problems without semi-strongly convex property. Numerical experiments
are conducted to demonstrate the high efficiency and robustness of our method.
