A proximal-based decomposition method for convex minimization problems
We present a new proximal based decomposition method for solving convex minimization problems. At each iteration, the algorithm computes two proximal steps in the dual variables and one proximal step in the primal variables. We derive this algorithm from Rockafellar`s proximal method of multipliers, which involves an augmented Lagrangian with an additional quadratic proximal term. The algorithm preserves the good features of the proximal method of multipliers, with the additional advantage that it leads to a decoupling of the constraints, and is thus suitable for parallel implementation. We allow for computing approximately the proximal minimization steps and we prove that, under mild assumptions on the problem`s data, the method is globally convergent at a linear rate. Furthermore, we extend our results to present a globally convergent method for computing saddle points of convex-concave saddle functions. We present numerical experiments with this method for solving projection problems on polytopes. Numerical results for randomly generated test problems over transportation and network polytopes with up to 200,000 variables indicate that this algorithm is efficient for large test problems.
- OSTI ID:
- 35895
- Report Number(s):
- CONF-9408161-; TRN: 94:009753-0158
- Resource Relation:
- Conference: 15. international symposium on mathematical programming, Ann Arbor, MI (United States), 15-19 Aug 1994; Other Information: PBD: 1994; Related Information: Is Part Of Mathematical programming: State of the art 1994; Birge, J.R.; Murty, K.G. [eds.]; PB: 312 p.
- Country of Publication:
- United States
- Language:
- English
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