A unified study of projection algorithms for solving Hilbertian convex feasibility
Numerous problems in applied mathematics, science, and engineering can be reduced to finding a common point of a collection of closed and convex sets in a Hilbert space. This abstract formulation is known as the hilbertian convex feasibility problem. The goal of this work is to study the convergence of a broad class of projection methods for solving hilbertian convex feasibility problems with a countable number of sets. A general algorithm is proposed which provides a unifying formulation for existing projection-based methods. It proceeds by extrapolated iterations of convex combinations of approximate projections onto subfamilies of sets. The relaxation parameters can vary over iteration- dependent, extrapolated ranges that extend beyond the interval [0, 2] usually used in projection methods. Various strategies are considered to control the order in which the sets are activated (cyclic, coercive, quasi-cyclic, admissible, chaotic). In addition, general regularity conditions on the sets are used (Slater condition, Levitin-Polyak condition, locally uniformly convex condition, bounded compactness, bounded and strong regularity) to study strong convergence. Weak convergence results for more general iterative schemes involving firmly nonexpansive operators instead of projections are also be presented.
- OSTI ID:
- 35912
- Report Number(s):
- CONF-9408161-; TRN: 94:009753-0176
- 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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