TY  - JOUR
U1  - Wissenschaftlicher Artikel
A1  - Tang, Tianyun
A1  - Toh, Kim-Chuan
T1  - Self-adaptive ADMM for semi-strongly convex problems
JF  - Mathematical Programming Computation
N2  - 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.
AB  - 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.
Y1  - 2023
SN  - 1867-2949
SS  - 1867-2949
U6  - https://doi.org/10.1007/s12532-023-00250-8
DO  - https://doi.org/10.1007/s12532-023-00250-8
VL  - 16
IS  - 1
SP  - 113
EP  - 150
S1  - 38
PB  - Springer Science and Business Media LLC
ER  -