A note on augmented Lagrangian-based parallel splitting method |
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Authors: | Kai?Wang Jitamitra?Desai Email author" target="_blank">Hongjin?HeEmail author |
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Institution: | 1.School of Mechanical and Aerospace Engineering,Nanyang Technological University,Singapore,Singapore;2.Department of Mathematics, School of Science,Hangzhou Dianzi University,Hangzhou,China |
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Abstract: | We consider the linearly constrained separable convex minimization problem, whose objective function consists of the sum of \(m\) individual convex functions in the absence of any coupling variables. While augmented Lagrangian-based decomposition methods have been well developed in the literature for solving such problems, a noteworthy requirement of these methods is that an additional correction step is a must to guarantee their convergence. This note shows that a straightforward Jacobian decomposition of the augmented Lagrangian method is globally convergent if the involved functions are further assumed to be strongly convex. |
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