The DOI matches its Crossref record; 16 of the 16 references it cites were found in a registry or an index.
The Exact Feasibility of Randomized Solutions of Uncertain Convex Programs
Abstract
Many optimization problems are naturally delivered in an uncertain framework, and one would like to exercise prudence against the uncertainty elements present in the problem. In previous contributions, it has been shown that solutions to uncertain convex programs that bear a high probability to satisfy uncertain constraints can be obtained at low computational cost through constraint randomization. In this paper, we establish new feasibility results for randomized algorithms. Specifically, the exact feasibility for the class of the so-called fully-supported problems is obtained. It turns out that all fully-supported problems share the same feasibility properties, revealing a deep kinship among problems of this class. It is further proven that the feasibility of the randomized solutions for all other convex programs can be bounded based on the feasibility for the prototype class of fully-supported problems. The feasibility result of this paper outperforms previous bounds and is not improvable because it is exact for fully-supported problems.
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Cites
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Robust solutions of uncertain linear programs
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The Scenario Approach to Robust Control Design
Calafiore, G. C., & Campi, M. C. (2006) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2006.875041 · Cited by 1,150
Self-citationRobust Solutions to Least-Squares Problems with Uncertain Data
El Ghaoui, L., & Lebret, H. (1997) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479896298130 · Cited by 1,076
Robust Solutions to Uncertain Semidefinite Programs
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Uncertain convex programs: randomized solutions and confidence levels
Calafiore, G., & Campi, M. C. (2005) · Mathematical Programming · doi:10.1007/s10107-003-0499-y · Cited by 659
Self-citationEfficient Monte Carlo Procedures for Generating Points Uniformly Distributed over Bounded Regions
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Robust Truss Topology Design via Semidefinite Programming
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Cited by
A Sampling-and-Discarding Approach to Chance-Constrained Optimization: Feasibility and Optimality
Campi, M. C., & Garatti, S. (2011) · Journal of Optimization Theory and Applications · doi:10.1007/s10957-010-9754-6 · Cited by 398
Self-citationThe scenario approach for systems and control design
Campi, M. C., Garatti, S., & Prandini, M. (2009) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2009.07.001 · Cited by 367
Self-citationOptimal Stochastic Coordinated Beamforming for Wireless Cooperative Networks With CSI Uncertainty
Shi, Y., Zhang, J., & Letaief, K. B. (2015) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2014.2385669 · Cited by 61
Formal Methods for Autonomous Systems
Wongpiromsarn, T., Ghasemi, M., Cubuktepe, M., Bakirtzis, G., Carr, S., Karabag, M. O., Neary, C., Gohari, P., & Topcu, U. (2023) · Foundations and Trends® in Systems and Control · doi:10.1561/2600000029 · Cited by 17
(2022) · doi:10.1109/isgt-europe54678.2022.9960351 · Cited by 14
Metadata
- Authors
- Campi, M. C., & Garatti, S.
- Venue
- SIAM Journal on Optimization
- Published
- 2008-01
- Volume
- 19
- Issue
- 3
- Pages
- 1211-1230
- ISSN
- 1052-6234 (ISSN-L)
- 1095-7189
- OpenAlex
- W1976466849
- Cited by
- 560
- References
- 16
- FWCI
- 21.01
- Type
- journal article
- Language
- en
- Open access
- closed
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