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Articles

Composite optimization for the resource allocation problem

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Pages 720-754 | Received 08 Mar 2019, Accepted 27 Dec 2019, Published online: 12 Feb 2020

References

  • A.S. Anikin, A.V. Gasnikov, P.E. Dvurechensky, A.I. Tyurin and A.V. Chernov, Dual approaches to the minimization of strongly convex functionals with a simple structure under affine constraints, Comput. Math. Math. Phys. 57 (2017), pp. 1262–1276. doi: 10.1134/S0965542517080048
  • K.J. Arrow and L. Hurwicz, Decentralization and computation in resource allocation, Stanford University, Department of Economics;1958.
  • J.P. Aubin, L'analyse non-linéaire et ses motivations économiques, Masson, Paris, 1984.
  • D.R. Baimurzina, A.V. Gasnikov, E.V. Gasnikova, P.E. Dvurechensky, E.I. Ershov, M.B. Kubentaeva and A.A. Lagunovskaya, Universal method of searching for equilibria and stochastic equilibria in transportation networks, Comput. Math. Math. Phys. 59 (2019), pp. 19–33. arXiv:1701.02473. doi: 10.1134/S0965542519010020
  • A. Bayandina, P. Dvurechensky, A. Gasnikov, F. Stonyakin and A. Titov, Mirror descent and convex optimization problems with non-smooth inequality constraints, in Large-Scale and Distributed Optimization, P. Giselsson and A. Rantzer, eds., chap. 8, Springer International Publishing, 2018, pp. 181–215, arXiv:1710.06612.
  • S. Boyd, N. Parikh, E. Chu, B. Peleato and J. Eckstein, Distributed optimization and statistical learning via the alternating direction method of multipliers, Found. Trends Mach. Learn. 3 (2011), pp. 1–122. http://dx.doi.org/10.1561/2200000016.
  • D.E. Campbell, Resource allocation mechanisms, Cambridge University Press, Cambridge, 1987.
  • A. Chernov, P. Dvurechensky and A. Gasnikov, Fast Primal-Dual Gradient Method for Strongly Convex Minimization Problems with Linear Constraints, Discrete Optimization and Operations Research: 9th International Conference, DOOR 2016, Vladivostok, Russia, September 19–23, 2016, Proceedings, Springer International Publishing, 2016, pp. 391–403.
  • J.C. Duchi, A. Agarwal and M.J. Wainwright, Dual averaging for distributed optimization: Convergence analysis and network scaling, IEEE. Trans. Automat. Contr. 57 (2012), pp. 592–606. doi: 10.1109/TAC.2011.2161027
  • D. Dvinskikh, E. Gorbunov, A. Gasnikov, P. Dvurechensky and C.A. Uribe, On Primal–Dual Approach for Distributed Stochastic Convex Optimization over Networks, 2019 IEEE Conference on Decision and Control (CDC), arXiv:1903.098442019.
  • P. Dvurechensky, A. Gasnikov and A. Kroshnin, Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm, Proceedings of the 35th International Conference on Machine Learning, Proceedings of Machine Learning Research, Vol. 80, arXiv:1802.04367, 2018, pp. 1367–1376.
  • P. Dvurechensky, A. Gasnikov, E. Gasnikova, S. Matsievsky, A. Rodomanov and I. Usik, Primal-Dual Method for Searching Equilibrium in Hierarchical Congestion Population Games, Supplementary Proceedings of the 9th International Conference on Discrete Optimization and Operations Research and Scientific School (DOOR 2016) Vladivostok, Russia, September 19–23, 2016, arXiv:1606.08988, 2016, pp. 584–595.
  • P. Dvurechensky, D. Dvinskikh, A. Gasnikov, C.A. Uribe and A. Nedić, Decentralize and Randomize: Faster Algorithm for Wasserstein Barycenters, Advances in Neural Information Processing Systems 31, NeurIPS 2018, arXiv:1806.03915, Curran Associates, Inc., 2018, pp. 10783–10793.
  • P.E. Dvurechensky, A.V. Gasnikov and A.A. Lagunovskaya, Parallel algorithms and probability of large deviation for stochastic convex optimization problems, Numer. Anal. Appl. 11 (2018), pp. 33–37. arXiv:1701.01830. doi: 10.1134/S1995423918010044
  • E.J. Friedman and S.S. Oren, The complexity of resource allocation and price mechanisms under bounded rationality, Economic Theory 6 (1995), pp. 225–250. doi: 10.1007/BF01212489
  • A. Gasnikov, Universal gradient descent, arXiv preprint arXiv:1711.00394 (2017).
  • S.V. Guminov, Y.E. Nesterov, P.E. Dvurechensky and A.V. Gasnikov, Accelerated primal-dual gradient descent with linesearch for convex, nonconvex, and nonsmooth optimization problems, Doklady Mathematics 99 (2019), pp. 125–128. doi: 10.1134/S1064562419020042
  • A. Ivanova, A. Gasnikov, E. Nurminski and E. Vorontsova, Walrasian equilibrium and centralized distributed optimization from the point of view of modern convex optimization methods on the example of resource allocation problem, Siberian J. Num. Math. 22 (2019), pp. 411–432. Sib. Branch of Russ. Acad. of Sci. Novosibirsk.
  • A. Ivanova, D. Pasechnyuk, P. Dvurechensky, A. Gasnikov and E. Vorontsova, Numerical methods for the resource allocation problem in networks, Comput. Math. Math. Phys. (2020), arXiv:1909.13321.
  • D. Jakovetić, J. Xavier and J.M.F. Moura, Fast distributed gradient methods, IEEE. Trans. Automat. Contr. 59 (2014), pp. 1131–1146. doi: 10.1109/TAC.2014.2298712
  • A. Kakhbod, Resource allocation in decentralized systems with strategic agents: an implementation theory approach, Springer Science & Business Media, New York, 2013.
  • A. Kroshnin, N. Tupitsa, D. Dvinskikh, P. Dvurechensky, A. Gasnikov and C. Uribe, On the Complexity of Approximating Wasserstein Barycenters, Proceedings of the 36th International Conference on Machine Learning, Proceedings of Machine Learning Research, Vol. 97, 09–15 Jun, arXiv:1901.08686, PMLR, Long Beach, CA, 2019, pp. 3530–3540.
  • A. Nedic and A. Ozdaglar, Distributed subgradient methods for multi-agent optimization, IEEE. Trans. Automat. Contr. 54 (2009), pp. 48–61. doi: 10.1109/TAC.2008.2009515
  • Y. Nesterov, Smooth minimization of non-smooth functions, Math. Program. 103 (2005), pp. 127–152. doi: 10.1007/s10107-004-0552-5
  • Y. Nesterov and V. Shikhman, Dual subgradient method with averaging for optimal resource allocation, Eur. J. Oper. Res. 270 (2018), pp. 907–916. doi: 10.1016/j.ejor.2017.09.043
  • B. Polyak, A general method of solving extremum problems, Soviet Math. Doklady 8 (1967), pp. 593–597.
  • D.B. Rokhlin, Resource allocation in communication networks with large number of users: stochastic gradient descent, Theory Probab. Appl. (2019), accepted.
  • K. Scaman, F. Bach, S. Bubeck, Y.T. Lee and L. Massoulié, Optimal Algorithms for Smooth and Strongly Convex Distributed Optimization in Networks, Proceedings of the 34th International Conference on Machine Learning, Proceedings of Machine Learning Research, Vol. 70, 06–11 Aug, PMLR, International Convention Centre, Sydney, Australia, 2017, pp. 3027–3036. Available at http://proceedings.mlr.press/v70/scaman17a.html.
  • K. Scaman, F. Bach, S. Bubeck, Y.T. Lee and L. Massoulié, Optimal convergence rates for convex distributed optimization in networks, J. Mach. Learn. Res. 20 (2019), pp. 1–31. , http://jmlr.org/papers/v20/19-543.html.
  • C.A. Uribe, D. Dvinskikh, P. Dvurechensky, A. Gasnikov and A. Nedić, Distributed Computation of Wasserstein Barycenters Over Networks, 2018 IEEE Conference on Decision and Control (CDC), arXiv:1803.02933, 2018, pp. 6544–6549.

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