This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Tupitsa, NazariiDvurechensky, PavelGasnikov, Alexander2022-06-302022-06-302020https://oa.tib.eu/renate/handle/123456789/9342https://doi.org/10.34657/8380We consider alternating minimization procedures for convex optimization problems with variable divided in many block, each block being amenable for minimization with respect to its variable with freezed other variables blocks. In the case of two blocks, we prove a linear convergence rate for alternating minimization procedure under Polyak-Łojasiewicz condition, which can be seen as a relaxation of the strong convexity assumption. Under strong convexity assumption in many-blocks setting we provide an accelerated alternating minimization procedure with linear rate depending on the square root of the condition number as opposed to condition number for the non-accelerated method.eng510Convex optimizationalternating minimizationblock-coordinate methodcomplexity analysisReport14 S.