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Distributed Banach-Picard Iteration: Application to Distributed EM and Distributed PCA
Francisco L. Andrade, Mário A. T. Figueiredo, João Xavier
In recent work, we proposed a distributed Banach-Picard iteration (DBPI) that allows a set of agents, linked by a communication network, to find a fixed point of a locally contract…
Distributed Banach-Picard Iteration for Locally Contractive Maps
Francisco L. Andrade, Mário A. T. Figueiredo, João Xavier
The Banach-Picard iteration is widely used to find fixed points of locally contractive (LC) maps. This paper extends the Banach-Picard iteration to distributed settings; specifical…
An Empirical Study of ADMM for Nonconvex Problems
Zheng Xu, Soham De, Mario Figueiredo +2
The alternating direction method of multipliers (ADMM) is a common optimization tool for solving constrained and non-differentiable problems. We provide an empirical study of the p…
Deconvolving Images with Unknown Boundaries Using the Alternating Direction Method of Multipliers
Mariana S. C. Almeida, Mário A. T. Figueiredo
The alternating direction method of multipliers (ADMM) has recently sparked interest as a flexible and efficient optimization tool for imaging inverse problems, namely deconvolutio…
Alternating Direction Algorithms for Constrained Sparse Regression: Application to Hyperspectral Unmixing
José M. Bioucas-Dias, Mário A. T. Figueiredo
Convex optimization problems are common in hyperspectral unmixing. Examples include: the constrained least squares (CLS) and the fully constrained least squares (FCLS) problems, wh…
Restoration of Poissonian Images Using Alternating Direction Optimization
Mário A. T. Figueiredo, José M. Bioucas-Dias
Much research has been devoted to the problem of restoring Poissonian images, namely for medical and astronomical applications. However, the restoration of these images using state…