  In this paper, we develop a self-adaptive ADMM that updates the penalty
parameter 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/k^2), 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 subproblem
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.
