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JOURNALS // Teoriya Veroyatnostei i ee Primeneniya

Teor. Veroyatnost. i Primenen., 2021, Volume 66, Issue 1, Pages 129–148 (Mi tvp5336)

Resource allocation in communication networks with large number of users: the dual stochastic gradient method
D. B. Rokhlin

References

1. A. Beck, Introduction to nonlinear optimization: theory, algorithms, and applications with MATLAB, MOS–SIAM Ser. Optim., 19, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA; Mathematical Optimization Society (MOS), Philadelphia, PA, 2014, xii+282 pp.  crossref  mathscinet  zmath
2. A. Beck, First-order methods in optimization, MOS–SIAM Ser. Optim., 25, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA; Mathematical Optimization Society (MOS), Philadelphia, PA, 2017, xii+475 pp.  crossref  mathscinet  zmath
3. A. Beck, A. Nedić, A. Ozdaglar, M. Teboulle, “An $O(1/k)$ gradient method for network resource allocation problems”, IEEE Trans. Control Netw. Syst., 1:1 (2014), 64–73  crossref  mathscinet  zmath
4. D. P. Bertsekas, Nonlinear programming, Athena Sci. Optim. Comput. Ser., 2nd ed., Athena Scientific, Belmont, MA, 1999, xiv+777 pp.  mathscinet  zmath
5. D. P. Bertsekas, Convex optimization theory, 2nd ed., Athena Scientific, Nashua, NH, 2009, x+246 pp.  mathscinet  zmath
6. Mung Chiang, S. H. Low, A. R. Calderbank, J. C. Doyle, “Layering as optimization decomposition: a mathematical theory of network architectures”, Proc. IEEE, 95:1 (2007), 255–312  crossref
7. E. Hazan, “Introduction to online convex optimization”, Foundations and Trends in Optimization, 2:3-4 (2016), 157–325  crossref
8. F. P. Kelly, A. K. Maulloo, D. K. H. Tan, “Rate control for communication networks: shadow prices, proportional fairness and stability”, J. Oper. Res. Soc., 49:3 (1998), 237–252  crossref
9. S. H. Low, D. E. Lapsley, “Optimization flow control. I. Basic algorithm and convergence”, IEEE/ACM Trans. Netw., 7:6 (1999), 861–874  crossref
10. A. Nedić, A. Ozdaglar, “Cooperative distributed multi-agent optimization”, Convex optimization in signal processing and communications, Ch. 10, Cambridge Univ. Press, Cambridge, 2010, 340–386  mathscinet  zmath
11. Yu. E. Nesterov, “{\vrule width0pt height8pt A method of solving a convex programming problem with convergence rate $O\bigl(\frac1{k^2}\bigr)$}”, Soviet Math. Dokl., 27 (1983), 372–376  mathnet  mathscinet  zmath
12. Yu. Nesterov, V. Shikhman, “Dual subgradient method with averaging for optimal resource allocation”, European J. Oper. Res., 270:3 (2018), 907–916  crossref  mathscinet  zmath
13. S. Shakkottai, R. Srikant, “Network optimization and control”, Foundations and Trends in Networking, 2:3 (2008), 271–379  crossref
14. R. Srikant, The mathematics of internet congestion control, Systems Control Found. Appl., Birkhäuser Boston, Inc., Boston, MA, 2004, xii+164 pp.  crossref  mathscinet  zmath
15. R. Srikant, Lei Ying, Communication networks. An optimization, control, and stochastic networks perspective, Cambridge Univ. Press, Cambridge, 2014, xii+352 pp.  mathscinet  zmath
16. Junshan Zhang, Dong Zheng, Mung Chiang, “The impact of stochastic noisy feedback on distributed network utility maximization”, IEEE Trans. Inform. Theory, 54:2 (2008), 645–665  crossref  mathscinet  zmath


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