An Optimal ADMM for Unilateral Obstacle Problems

An Optimal ADMM for Unilateral Obstacle Problems

Blog Article

We propose a new alternating direction method of Disposable Skewers multipliers (ADMM) with an optimal parameter for the unilateral obstacle problem.We first use the five-point difference scheme to discretize the problem.Then, we present an augmented Lagrangian by introducing an auxiliary unknown, and an ADMM is applied to the corresponding saddle-point problem.Through eliminating the primal and auxiliary unknowns, a pure dual algorithm is then used.The convergence of the proposed method is analyzed, and a simple strategy is presented for selecting the optimal parameter, with the largest and smallest eigenvalues of Hats the iterative matrix.

Several numerical experiments confirm the theoretical findings of this study.