We consider the linearly constrained separable convex programming, whose objective function is separable into m individual convex functions without coupled variables. The alternating direction method of multipliers has been well studied in the literature for the special case m=2, while it remains open whether its convergence can be extended to the general case m ≥3. This note shows the global convergence of this extension when the involved functions are further assumed to be strongly convex.
Scopus Subject Areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics
- Alternating direction method of multipliers
- Global convergence
- Strongly convex functions