Sweeping by a tame process

2014/12/30 by Daniilidis, Aris, Drusvyatskiy, Dmitriy
#14P10 #49J53 #FOS: Mathematics #Optimization and Control (math.OC) #Primary 34A60 #Secondary 34A26

paper · doi:10.48550/arxiv.1412.8581

Abstract

We show that any semi-algebraic sweeping process admits piecewise absolutely continuous solutions, and any such bounded trajectory must have finite length. Analogous results hold more generally for sweeping processes definable in o-minimal structures. This extends previous work on (sub)gradient dynamical systems beyond monotone sweeping sets.

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