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On the Linear Convergence of Descent Methods for Convex Essentially Smooth Minimization
Abstract
Consider the problem of minimizing, over a polyhedral set, the composition of an affine mapping with a strictly convex essentially smooth function. A general result on the linear convergence of descent methods for solving this problem is presented. By applying this result, the linear convergence of both the gradient projection algorithm of Goldstein and Levitin and Polyak, and a matrix splitting algorithm using regular splitting, is established. The results do not require that the cost function be strongly convex or that the optimal solution set be bounded. The key to the analysis lies in a new error bound for estimating the distance from a feasible point to the optimal solution set.
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Citations
Cited by
Error bounds in mathematical programming
Pang, J.-S. (1997) · Mathematical Programming · doi:10.1007/bf02614322 · Cited by 441
Error bounds and convergence analysis of feasible descent methods: a general approach
Luo, Z.-Q., & Tseng, P. (1993) · Annals of Operations Research · doi:10.1007/bf02096261 · Cited by 420
Self-citationLinear Convergence Rate of a Class of Distributed Augmented Lagrangian Algorithms
Jakovetic, D., Moura, J. M. F., & Xavier, J. (2015) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2014.2363299 · Cited by 123
Metadata
- Authors
- Luo, Z.-Q., & Tseng, P.
- Venue
- SIAM Journal on Control and Optimization
- Published
- 1992-03
- Volume
- 30
- Issue
- 2
- Pages
- 408-425
- ISSN
- 0363-0129 (ISSN-L)
- 1095-7138
- OpenAlex
- W2090084467
- Cited by
- 190
- References
- 0
- FWCI
- 9.31
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: On the Linear Convergence of Descent Methods for Convex Essentially Smooth Minimization. https://app.cochat.ai/papers/10.1137/0330025
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- Luo, Z.-Q., & Tseng, P. (1992). On the Linear Convergence of Descent Methods for Convex Essentially Smooth Minimization. SIAM Journal on Control and Optimization. https://doi.org/10.1137/0330025
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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