Alternating direction method of multiplier for the unilateral contact problem with an automatic penalty parameter selection

In this paper, we propose a symmetric alternating method of multipliers for minimizing the sum of two nonconvex functions with linear constraints, which contains the classic alternating direction method of multipliers in the algorithm framework. Based on the powerful Kurdyka–Łojasiewicz property, and under some assumptions about the penalty parameter and objective function, we prove that each bounded sequence generated by the proposed method globally converges to a critical point of the augmented Lagrangian function associated with the given problem. Moreover, we report some preliminary numerical results on solving [Formula: see text] regularized sparsity optimization and nonconvex feasibility problems to indicate the feasibility and effectiveness of the proposed method.

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.740.929 ◽

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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Optimal Parameter Selection for the Alternating Direction Method of Multipliers (ADMM): Quadratic Problems

IEEE Transactions on Automatic Control ◽

10.1109/tac.2014.2354892 ◽

2015 ◽

Vol 60 (3) ◽

pp. 644-658 ◽

Cited By ~ 192

Author(s):

Euhanna Ghadimi ◽

Andre Teixeira ◽

Iman Shames ◽

Mikael Johansson

Keyword(s):

Optimal Parameter ◽

Parameter Selection ◽

Alternating Direction Method ◽

Method Of Multipliers ◽

Alternating Direction ◽

Selection For ◽

Optimal Parameter Selection

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Iteration Complexity of the Alternating Direction Method of Multipliers for Quasi-Separable Problems in Multi-Disciplinary Design Optimization

Volume 2B: 40th Design Automation Conference ◽

10.1115/detc2014-35066 ◽

2014 ◽

Author(s):

Ning Quan ◽

Harrison Kim

Keyword(s):

Design Optimization ◽

Model Fitting ◽

Alternating Direction Method ◽

Method Of Multipliers ◽

Penalty Parameter ◽

Proximal Point ◽

Alternating Direction ◽

Separable Problems ◽

Admm Algorithm ◽

Parameter Scheme

The Alternating Direction Method of Multipliers (ADMM) is a distributed algorithm suitable for quasi-separable problems in Multi-disciplinary Design Optimization. Previous authors have studied the convergence and complexity of the ADMM algorithm by treating it as an instance of the proximal point algorithm. In this paper, those previous results are extended to an alternate form of the ADMM algorithm applied to the quasi-separable problem. Secondly, a dynamic penalty parameter updating heuristic for the ADMM algorithm is introduced and compared against a previously proposed updating heuristic. The proposed updating heuristic was tested on a distributed linear model fitting example and performed favorably against the other heuristic and the fixed penalty parameter scheme.

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