An extended alternating direction method for variational inequality problems with linear equality and inequality constraints

2007 ◽  
Vol 184 (2) ◽  
pp. 769-782 ◽  
Author(s):  
Zhong Zhou ◽  
Anthony Chen ◽  
Deren Han
Keyword(s):  
Variational Inequality ◽  
Inequality Constraints ◽  
Alternating Direction Method ◽  
Variational Inequality Problems ◽  
Linear Equality ◽  
Alternating Direction ◽  
Equality And Inequality Constraints

The Engineering Application of Improved Alternating Direction Method for Solving Power Systems Multi-Area Dispatch Problem

2015 ◽  
Vol 740 ◽  
pp. 929-932
Author(s):  
Ya Ming Ren ◽  
Shu Min Fei ◽  
Hai Kun Wei
Keyword(s):  
Power Systems ◽  
Economic Dispatch ◽  
Engineering Application ◽  
Inequality Constraints ◽  
Alternating Direction Method ◽  
Penalty Parameter ◽  
Alternating Direction ◽  
Equality And Inequality Constraints ◽  
Convergence Performance ◽  
Consistency Constraint

The alternating direction method has been widespread used to solve multi-area economic dispatch problem. Compared with traditional centered economic dispatch, alternating direction method divides centered optimal problem into completely independent sub-problems while the corresponding equality and inequality constraints are satisfied. However, plenty of applications show that the choice of penalty parameter for the consistency constraint has an important influence on the convergence performance of alternating direction method. In this paper, we proposed a novel improved alternating direction method. To be more exact, the key is to adjust penalty parameter based on iterative information of alternating direction method. Numerical results illustrate the proposed method has better stability in convergence.

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