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- W2893585154 abstract "We develop and analyze a new `relax-and-split' (RS) approach for compositions of separable nonconvex nonsmooth functions with linear maps. RS uses a relaxation technique together with partial minimization, and brings classic techniques including direct factorization, matrix decompositions, and fast iterative methods to bear on nonsmooth nonconvex problems. We also extend the approach to trimmed nonconvex-composite formulations; the resulting Trimmed RS (TRS) can fit models while detecting outliers in the data. We then test RS and TRS on a diverse set of applications: (1) phase retrieval, (2) stochastic shortest path problems, (3) semi-supervised classification, and (4) new clustering approaches. RS/TRS can be applied to models with very weak functional assumptions, are easy to implement, competitive with existing methods, and enable a new level of modeling formulations to be put forward to address emerging challenges in the mathematical sciences." @default.
- W2893585154 created "2018-10-05" @default.
- W2893585154 creator A5072154999 @default.
- W2893585154 creator A5091863515 @default.
- W2893585154 date "2018-02-07" @default.
- W2893585154 modified "2023-09-27" @default.
- W2893585154 title "Relax-and-split method for nonsmooth nonconvex problems" @default.
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