Abstract
The discussion about non-centralized MPC schemes for economic dispatch is started by presenting two distributed optimization algorithms that solve Problem (2.15). The proposed methods are based on the augmented Lagrangian approach. First, in Sect. 3.1, a brief introduction about the augmented Lagrangian approach is presented. Then, in Sect. 3.2, a distributed algorithm based on this approach is designed and its convergence properties are stated. Section 3.3 discusses another distributed algorithm based on the ADMM, which also belongs to the class of the augmented Lagrangian methods. Similarly, the design and convergence analysis of the second algorithm is provided. Finally, some comparisons of the proposed algorithms and conclusions are drawn in Sect. 3.4.
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References
Bertsekas DP (2008) Extended monotropic programming and duality. J Optim Theory Appl 139(2):209–225
Boyd S, Parikh N, Chu E, Peleato B, Eckstein J (2011) Distributed optimization and statistical learning via the alternating direction method of multipliers. Found Trends Mach Learn 3(1):1–122
Boyd S, Vandenberghe L (2010) Convex optimization, vol 25. Cambridge University Press, Cambridge
Bertsekas DP (1995) Nonlinear programming. Athena Scientific
Larsen GKH, van Foreest ND, Scherpen JMA (2014) Distributed MPC applied to a network of households with micro-CHP and heat storage. IEEE Trans Smart Grid 5(4):2106–2114
Kraning M, Chu E, Lavaei J, Boyd S (2014) Dynamic network energy management via proximal message passing. Found Trends in Optim 1(2):73–126
Wang T, O’Neill D, Kamath H (2015) Dynamic control and optimization of distributed energy resources in a microgrid. IEEE Trans Smart Grid 6(6):2884–2894
Hans CA, Braun P, Raisch, J, Grune L, Reincke-Collon C (2019) Hierarchical distributed model predictive control of interconnected microgrids. IEEE Trans Sustain Energy 10(1):407–416
Nedić A, Ozdaglar A (2009) Distributed subgradient methods for multi-agent optimization. IEEE Trans Autom Control 54(1):48–61
Nedić A, Ozdaglar A, Parrilo PA (2010) Constrained consensus and optimization in multi-agent networks. IEEE Trans Autom Control 55(4):922–938
Chang T (2016) A proximal dual consensus ADMM method for multi-agent constrained optimization. IEEE Trans Signal Process 64(14):3719–3734
Chatzipanagiotis N, Dentcheva D, Zavlanos MM (2015) An augmented Lagrangian method for distributed optimization. Math Program 152(1):405–434
Chatzipanagiotis N, Zavlanos MM (2016) A distributed algorithm for convex constrained optimization under noise. IEEE Trans Autom Control 61(9):2496–2511
Lee S, Chatzipanagiotis N, Zavlanos MM (2018) Complexity certification of a distributed augmented Lagrangian method. IEEE Trans Autom Control 63(3):827–834
Mulvey JM, Ruszczyński A (1992) A diagonal quadratic approximation method for large scale linear programs. Oper Res Lett 12(4):205–215
Berger A, Mulvey J, Ruszczyński A (1994) An extension of the DQA algorithm to convex stochastic programs. SIAM J Optim 4(4):735–753
Ruszczyński A (1995) On convergence of an augmented Lagrangian decomposition method for sparse convex optimization. Math Oper Res 20(3):634–656
Bertsekas DP, Tsitsiklis JN (1997) Parallel and distributed computation: numerical methods. Athena Scientific
Wei E, Ozdaglar A (2013) On the O(1/k) convergence of asynchronous distributed alternating direction method of multipliers, pp 1–30. ar**v:1307.8254
Chang T, Hong M, Liao W, Wang X (2016) Asynchronous distributed ADMM for large-scale optimization—part I: Algorithm and convergence analysis. IEEE Trans Signal Process 64(12):3118–3130
Beck A (2017) First-order methods in optimization. Society for Industrial and Applied Mathematics
Nedić A (2008) Lecture notes optimization I. Hamilton Institute
Uribe CA, Lee S, Gasnikov A, Nedić A (2018) A dual approach for optimal algorithms in distributed optimization over networks, pp 1–37. ar**v:1809.00710
Nesterov Y, Nemirovskii A (1994) Interior-point polynomial algorithms in convex programming, vol 13. SIAM
Nesterov Y (2013) Introductory lectures on convex optimization: a basic course, vol 87. Springer Science & Business Media, Berlin
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Ananduta, W.W. (2022). Distributed Augmented Lagrangian Methods. In: Non-centralized Optimization-Based Control Schemes for Large-Scale Energy Systems. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-89803-8_3
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