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- W4225518087 abstract "In this work, we present a generic step-size choice for the ADMM type proximal algorithms. It admits a closed-form expression and is theoretically optimal with respect to a worst-case convergence rate bound. It is simply given by the ratio of Euclidean norms of the dual and primal solutions, i.e., $ ||{lambda}^star|| / ||{x}^star||$. Numerical tests show that its practical performance is near-optimal in general. The only challenge is that such a ratio is not known a priori and we provide two strategies to address it. The derivation of our step-size choice is based on studying the fixed-point structure of ADMM using the proximal operator. However, we demonstrate that the classical proximal operator definition contains an input scaling issue. This leads to a scaled step-size optimization problem which would yield a false solution. Such an issue is naturally avoided by our proposed new definition of the proximal operator. A series of its properties is established." @default.
- W4225518087 created "2022-05-05" @default.
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- W4225518087 date "2022-04-06" @default.
- W4225518087 modified "2023-10-17" @default.
- W4225518087 title "A Generic Closed-form Optimal Step-size for ADMM" @default.
- W4225518087 doi "https://doi.org/10.48550/arxiv.2204.02642" @default.
- W4225518087 hasPublicationYear "2022" @default.
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