On the O(1/n) Convergence Rate of the Auxiliary Problem Principle for Separable Convex Programming and Its Application to the Power Systems Multi-Area Economic Dispatch Problem

The auxiliary problem principle has been widely applied in power systems to solve the multi-area economic dispatch problem. Although the effectiveness and correctness of the auxiliary problem principle method have been demonstrated in relevant literatures, the aspect connected with accurate estimate of its convergence rate has not yet been established. In this paper, we prove the O ( 1 / n ) convergence rate of the auxiliary problem principle method.

[1]  Q. Jiang,et al.  Parallel augment Lagrangian relaxation method for transient stability constrained unit commitment , 2013, IEEE Transactions on Power Systems.

[2]  Yuan Shen,et al.  On the O(1/t) convergence rate of Ye-Yuan's modified alternating direction method of multipliers , 2014, Appl. Math. Comput..

[3]  B. He,et al.  Alternating Direction Method with Self-Adaptive Penalty Parameters for Monotone Variational Inequalities , 2000 .

[4]  B. H. Kim,et al.  A comparison of distributed optimal power flow algorithms , 2000 .

[5]  Bingsheng He,et al.  On the O(1/n) Convergence Rate of the Douglas-Rachford Alternating Direction Method , 2012, SIAM J. Numer. Anal..

[6]  Hong-Chan Chang,et al.  Large-scale economic dispatch by genetic algorithm , 1995 .

[7]  Wanxing Sheng,et al.  The decomposition and computation method for distributed optimal power flow based on message passing interface (MPI) , 2011 .

[8]  G. Cohen.  Auxiliary problem principle and decomposition of optimization problems , 1980 .

[9]  A. Renaud,et al.  Daily generation scheduling optimization with transmission constraints: a new class of algorithms , 1992 .

[10]  Don Hur,et al.  Distributed implementation of generation scheduling algorithm on interconnected power systems , 2011 .

[11]  Ross Baldick,et al.  Coarse-grained distributed optimal power flow , 1997 .

[12]  Arkadi Nemirovski,et al.  Prox-Method with Rate of Convergence O(1/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems , 2004, SIAM J. Optim..

[13]  Bingsheng He,et al.  On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators , 2013, Computational Optimization and Applications.

[14]  C. Beltran,et al.  Unit Commitment by Augmented Lagrangian Relaxation: Testing Two Decomposition Approaches , 2002 .