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Ìâ Ä¿£ºAccuracy vs Implementability in Algorithmic Design—An Example of Operator Splitting Methods for Convex OptimizationËã·¨Éè¼ÆÖÐÈôºÎ˼¿¼¾«¶ÈºÍ¿É²Ù×÷ÐÔ—ÒÔ͹ÓÅ»¯ÎÊÌâµÄËã×Ó¸îÁѲ½ÖèΪÀý
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Accuracy and implementability are two common yet usually conflicted objectives for developing an efficient algorithm. In this talk, I will focus on the context of convex optimization models with separable structures to show how to make a trade-off between these two objectives for some operator splitting methods originated from the PDE literature (e.g., the Douglas-Rachford and Peaceman-Rachford schemes) The resulting algorithms could be applicable to large-scale dataset; and their efficiency will be demonstrated by some specific applications in statistical learning and image processing (e.g., the LASSO and TV-deblurring models). Some theoretical results such as the convergence rates of these algorithms will also be mentioned briefly.
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