The DOI matches its Crossref record; 19 of the 19 references it cites were found in a registry or an index.
Interior Gradient and Proximal Methods for Convex and Conic Optimization
Abstract
Interior gradient (subgradient) and proximal methods for convex constrained minimization have been much studied, in particular for optimization problems over the nonnegative octant. These methods are using non-Euclidean projections and proximal distance functions to exploit the geometry of the constraints. In this paper, we identify a simple mechanism that allows us to derive global convergence results of the produced iterates as well as improved global rates of convergence estimates for a wide class of such methods, and with more general convex constraints. Our results are illustrated with many applications and examples, including some new explicit and simple algorithms for conic optimization problems. In particular, we derive a class of interior gradient algorithms which exhibits an $O(k^{-2})$ global convergence rate estimate.
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Cites
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Monotone Operators and the Proximal Point Algorithm
Rockafellar, R. T. (1976) · SIAM Journal on Control and Optimization · doi:10.1137/0314056 · Cited by 3,559
Minimization Methods for Non-Differentiable Functions
Shor, N. Z. (1985) · Springer Series in Computational Mathematics · doi:10.1007/978-3-642-82118-9 · Cited by 1,551
Mirror descent and nonlinear projected subgradient methods for convex optimization
Beck, A., & Teboulle, M. (2003) · Operations Research Letters · doi:10.1016/s0167-6377(02)00231-6 · Cited by 1,060
Self-citationOn the Convergence of the Proximal Point Algorithm for Convex Minimization
Güler, O. (1991) · SIAM Journal on Control and Optimization · doi:10.1137/0329022 · Cited by 681
Problem Complexity and Method Efficiency in Optimization
Darzentas, J., Nemirovsky, A., & Yudin, D. B. (1984) · Journal of the Operational Research Society · doi:10.2307/2581380 · Cited by 650
On the Goldstein-Levitin-Polyak gradient projection method
Bertsekas, D. P. (1976) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1976.1101194 · Cited by 583
Convergence Analysis of a Proximal-Like Minimization Algorithm Using Bregman Functions
Chen, G., & Teboulle, M. (1993) · SIAM Journal on Optimization · doi:10.1137/0803026 · Cited by 428
Self-citationNonlinear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming
Eckstein, J. (1993) · Mathematics of Operations Research · doi:10.1287/moor.18.1.202 · Cited by 324
Poudat, F.-X. (2011) · Sexualité, Couple et Tcc. Volume 1 : les Difficultés Sexuelles · doi:10.1016/b978-2-294-71119-0.00006-6 · Cited by 304
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Templates for convex cone problems with applications to sparse signal recovery
Becker, S. R., Candès, E. J., & Grant, M. C. (2011) · Mathematical Programming Computation · doi:10.1007/s12532-011-0029-5 · Cited by 608
Subgradient Methods for Saddle-Point Problems
Nedić, A., & Ozdaglar, A. (2009) · Journal of Optimization Theory and Applications · doi:10.1007/s10957-009-9522-7 · Cited by 438
An optimal method for stochastic composite optimization
Lan, G. (2012) · Mathematical Programming · doi:10.1007/s10107-010-0434-y · Cited by 427
Fast $\ell_{1}$-Minimization Algorithms for Robust Face Recognition
Yang, A. Y., Zhou, Z., Balasubramanian, A. G., Sastry, S. S., & Ma, Y. (2013) · IEEE Transactions on Image Processing · doi:10.1109/tip.2013.2262292 · Cited by 341
Ghadimi, S., & Lan, G. (2012) · SIAM Journal on Optimization · doi:10.1137/110848864 · Cited by 269
Metadata
- Authors
- Auslender, A., & Teboulle, M.
- Venue
- SIAM Journal on Optimization
- Published
- 2006-01
- Volume
- 16
- Issue
- 3
- Pages
- 697-725
- ISSN
- 1052-6234 (ISSN-L)
- 1095-7189
- OpenAlex
- W1986891697
- Cited by
- 269
- References
- 19
- FWCI
- 6.83
- Type
- journal article
- Language
- en
- Open access
- closed
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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).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
