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Non-smooth Non-convex Bregman Minimization: Unification and new Algorithms |
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Abstract: We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate (Bregman) proximal point of the convex model. This approximate minimizer of the model function yields a descent direction, along which the next iterate is found. Complemented with an Armijo-like line search strategy, we obtain a flexible algorithm for which we prove (subsequential) convergence to a stationary point under weak assumptions on the growth of the model function error. Special instances of the algorithm with a Euclidean distance function are, for example, Gradient Descent, Forward--Backward Splitting, ProxDescent, without the common requirement of a "Lipschitz continuous gradient". In addition, we consider a broad class of Bregman distance functions (generated by Legendre functions) replacing the Euclidean distance. The algorithm has a wide range of applications including many linear and non-linear inverse problems in image processing and machine learning. |
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| arXiv |
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Latest update: 10.07.2017 |
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Citation: P. Ochs, J. Fadili, T. Brox: Non-smooth Non-convex Bregman Minimization: Unification and new Algorithms. ![[pdf]](/images/pdf_14x14.png) Journal of Optimization Theory and Applications, 181(1):244-278, 2018. |
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Bibtex: @article{OFB18, title = {Non-smooth Non-convex Bregman Minimization: Unification and new Algorithms}, author = {P. Ochs and J. Fadili and T. Brox}, year = {2018}, journal = {Journal of Optimization Theory and Applications}, number = {1}, volume = {181}, pages = {244--278} } |
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