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ProxToolbox: A Labortatory for Quantitative Convergence Analysis of Picard Iterations

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ProxToolbox: A Labortatory for Quantitative Convergence Analysis of Picard Iterations
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30
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Any casual observer of preprint servers like arXiv wil have noticed the weekly and sometimes daily appearance of new first-oder methods for structured optimization and (convex )relaxations for popular problems. Absent from this surge in new algorithmic strategies is any standard test-bed of real-world problems for trustworthy comparisons. The phase retrieval problem is one example of this sometimes absurd disconnect between proposed algorithms and the problems these routines are meant to solve. The ProxToolbox started as an effort to establish reproducibility of my numerical experiments, not only for students and other researchers, but for myself twenty years hence. It has since developed into what I hope to convince you is a platform for testing and comparing prox-based methods on data sets, both simulated and experimental, from some of the more popular applications of first order methods.