Random block-coordinate methods for inconsistent convex optimisation problems

Facchinei, F., Kanzow, C.: Generalized Nash equilibrium problems. 4OR 5, 173–210 (2007)

Grasmair, M., Haltmeier, M., Scherzer, O.: The residual method for regularizing ill-posed problems. Appl. Math. Comput. 218(6), 2693–2710 (2011). https://doi.org/10.1016/j.amc.2011.08.009

Wood, A.J., Wollenberg, B.F., Sheblé, G.B.: Power Generation, Operation, and Control. Wiley, New York (2013)

Bienstock, D.: Electrical Transmission System Cascades and Vulnerability: An Operations Research Viewpoint. MOS-SIAM Series on Optimization (2015)

Papavasiliou, A.: Analysis of distribution locational marginal prices. IEEE Trans. Smart Grid 9(5), 4872–4882 (2018). https://doi.org/10.1109/TSG.2017.2673860

Nesterov, Y.: Efficiency of coordinate descent methods on huge-scale optimization problems. SIAM J. Optim. 22(2), 341–362 (2012)

Lu, Z., Xiao, L.: On the complexity analysis of randomized block-coordinate descent methods. Math. Program. 152(1), 615–642 (2015). https://doi.org/10.1007/s10107-014-0800-2

Richtárik, P., Takáč, M.: Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function. Math. Program. 144(1), 1–38 (2014). https://doi.org/10.1007/s10107-012-0614-z

Richtárik, P., Takáč, M.: Parallel coordinate descent methods for big data optimization. Math. Program. 156(1–2), 433–484 (2016)

Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualitéd’une classe de problèmes de dirichlet non linéaires. Rev. Fr. Autom. Inform. Rech. Opér., Anal. Numér. 9(R2), 41–76 (1975)

Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Comput. Math. Appl. 2(1), 17–40 (1976). https://doi.org/10.1016/0898-1221(76)90003-1

Han, D., Sun, D., Zhang, L.: Linear rate convergence of the alternating direction method of multipliers for convex composite programming. Math. Oper. Res. 43(2), 622–637 (2017). https://doi.org/10.1287/moor.2017.0875

Eckstein, J., Yao, W.: Understanding the convergence of the alternating direction method of multipliers: theoretical and computational perspectives. Pac. J. Optim. 11(4), 619–644 (2015)

Chen, C., He, B., Ye, Y., Yuan, X.: The direct extension of admm for multi-block convex minimization problems is not necessarily convergent. Math. Program. 155(1), 57–79 (2016). https://doi.org/10.1007/s10107-014-0826-5

Gao, X., Xu, Y.-Y., Zhang, S.-Z.: Randomized primal–dual proximal block coordinate updates. J. Oper. Res. Soc. China 7(2), 205–250 (2019)

Gao, X., Zhang, S.-Z.: First-order algorithms for convex optimization with nonseparable objective and coupled constraints. J. Oper. Res. Soc. China 5(2), 131–159 (2017). https://doi.org/10.1007/s40305-016-0131-5

Deng, W., Lai, M.-J., Peng, Z., Yin, W.: Parallel multi-block ADMM with $o(1 / k)$ convergence. J. Sci. Comput. 71(2), 712–736 (2016). https://doi.org/10.1007/s10915-016-0318-2

Nesterov, Y.: A method of solving a convex programming problem with convergence rate $o(1/k^{2})$. Sov. Math. Dokl. 27(2), 372–376 (1983)

Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2(1), 183–202 (2009). https://doi.org/10.1137/080716542

Nesterov, Y.: Gradient methods for minimizing composite functions. Math. Program. 140(1), 125–161 (2013). https://doi.org/10.1007/s10107-012-0629-5

Kang, M., Kang, M., Jung, M.: Inexact accelerated augmented Lagrangian methods. Comput. Optim. Appl. 62(2), 373–404 (2015). https://doi.org/10.1007/s10589-015-9742-8

Malitsky, Y.: The primal-dual hybrid gradient method reduces to a primal method for linearly constrained optimization problems (2019)

Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40(1), 120–145 (2011). https://doi.org/10.1007/s10851-010-0251-1

Tseng, P.: On accelerated proximal gradient methods for convex-concave optimization (2008)

Malitsky, Y.: Chambolle-Pock and Tseng’s methods: relationship and extension to the bilevel optimization (2017)

Luke, D.R., Malitsky, Y.: Block-coordinate primal-dual method for nonsmooth minimization over linear constraints. In: Giselsson, P., Rantzer, A. (eds.) Large-Scale and Distributed Optimization, pp. 121–147. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-97478-1_6

Tran-Dinh, Q., Liu, D.: Faster randomized primal-dual algorithms for nonsmooth composite convex minimization. arXiv preprint (2020) arXiv:2003.01322

Xu, Y., Zhang, S.: Accelerated primal-dual proximal block coordinate updating methods for constrained convex optimization. Comput. Optim. Appl. 70(1), 91–128 (2018). https://doi.org/10.1007/s10589-017-9972-z

Tran-Dinh, Q., Liu, D.: A new randomized primal-dual algorithm for convex optimization with fast last iterate convergence rates. Optim. Methods Softw. 38(1), 184–217 (2023). https://doi.org/10.1080/10556788.2022.2119233

Farivar, M., Low, S.H.: Branch flow model: relaxations and convexification—part I. IEEE Trans. Power Syst. 28(3), 2554–2564 (2013). https://doi.org/10.1109/TPWRS.2013.2255317

Peng, Q., Low, S.H.: Distributed optimal power flow algorithm for radial networks, I: balanced single phase case. IEEE Trans. Smart Grid 9(1), 111–121 (2018). https://doi.org/10.1109/TSG.2016.2546305

Fercoq, O., Richtárik, P.: Accelerated, parallel, and proximal coordinate descent. SIAM J. Optim. 25(4), 1997–2023 (2015). https://doi.org/10.1137/130949993

Ryu, E.K., Yin, W.: Large-Scale Convex Optimization: Algorithms & Analyses via Monotone Operators. Cambridge University Press, Cambridge (2022). https://doi.org/10.1017/9781009160865

Qu, Z., Richtárik, P.: Coordinate descent with arbitrary sampling I: algorithms and complexity. Optim. Methods Softw. 31(5), 829–857 (2016). https://doi.org/10.1080/10556788.2016.1190360

Qu, Z., Richtárik, P.: Coordinate descent with arbitrary sampling II: expected separable overapproximation. Optim. Methods Softw. 31(5), 858–884 (2016). https://doi.org/10.1080/10556788.2016.1190361

Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011)

Necoara, I., Clipici, D.: Efficient parallel coordinate descent algorithm for convex optimization problems with separable constraints: application to distributed MPC. J. Process Control 23(3), 243–253 (2013)

Bianchi, P., Hachem, W., Iutzeler, F.: A coordinate descent primal-dual algorithm and application to distributed asynchronous optimization. IEEE Trans. Autom. Control 61(10), 2947–2957 (2015)

Fercoq, O., Bianchi, P.: A coordinate-descent primal-dual algorithm with large step size and possibly nonseparable functions. SIAM J. Optim. 29(1), 100–134 (2019). https://doi.org/10.1137/18M1168480

Latafat, P., Freris, N.M., Patrinos, P.: A new randomized block-coordinate primal-dual proximal algorithm for distributed optimization. IEEE Trans. Autom. Control 64(10), 4050–4065 (2019)

Nesterov, Y.: Lectures on Convex Optimization. Springer Optimization and Its Applications, vol. 137. Springer, Berlin (2018)

d’Aspremont, A., Scieur, D., Taylor, A.: Acceleration methods. Found. Trends Optim. 5(1–2), 1–245 (2021)

Bilenne, O., Jacquot, P., Oudjane, N., Staudigl, M., Wan, C.: A privacy-preserving distributed computational approach for distributed locational marginal prices. In: 61st IEEE Conference on Decision and Control (2022)

Baran, M.E., Wu, F.F.: Optimal capacitor placement on radial distribution systems. IEEE Trans. Power Deliv. 4(1), 725–734 (1989). https://doi.org/10.1109/61.19265

Molzahn, D.K., Hiskens, I.A.: A survey of relaxations and approximations of the power flow equations. Found. Trends Electr. Energy Syst. 4(1–2), 1–221 (2019). https://doi.org/10.1561/3100000012

Gan, L., Li, N., Topcu, U., Low, S.H.: Exact convex relaxation of optimal power flow in radial networks. IEEE Trans. Autom. Control 60(1), 72–87 (2015). https://doi.org/10.1109/TAC.2014.2332712

Mezghani, I., Misra, S., Deka, D.: Stochastic ac optimal power flow: a data-driven approach. Electr. Power Syst. Res. 189, 106567 (2020)

Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, Berlin (2016)

Robbins, H., Siegmund, D.: A convergence theorem for non negative almost supermartingales and some applications. In: Rustagi, J.S. (ed.) Optimizing Methods in Statistics, pp. 233–257. Academic Press, San Diego (1971). https://doi.org/10.1016/B978-0-12-604550-5.50015-8. https://www.sciencedirect.com/science/article/pii/B9780126045505500158