A smoothing alternating minimization-based algorithm for clustering with sum-min of Euclidean norms

SHOHAM Sabach, MARC Teboulle, SERGEY Voldman

Research output: Contribution to journalArticlepeer-review


We consider the problem of minimizing an objective function defined as the finite sum of a minimum collection of nonsmooth
and convex functions, which includes the fundamental clustering problem as a particular case. To tackle this nonsmooth and nonconvex problem, we develop a smoothing alternating minimization-based algorithm
(SAMBA), which is proven to globally converge to a critical point of
the smoothed problem. We then show how it can be applied to the
clustering problem with adequate smoothing functions, producing two
very simple algorithms resembling the so-called k-means algorithm, with
global convergence analysis.
Original languageUndefined/Unknown
Pages (from-to)653-679
Number of pages27
JournalPure and applied functional analysis
Issue number4
StatePublished - 2018

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