Convergence Order of a Numerical Scheme for Sweeping Process
Frédéric Bernicot, Juliette Venel · SIAM Journal on Control and Optimization · 2013
In [J. Venel, Numer. Math., 118 (2011), pp. 367--400], an implementable algorithm was introduced to compute discrete solutions of sweeping processes (i.e., specific first order differential inclusions). The convergence of this numerical scheme was proved thanks to compactness arguments. Here we establish that this algorithm is of order $\frac{1}{2}$. The considered sweeping process involves a set-valued map given by a finite number of inequality constraints. The proof rests on a metric qualification condition between the sets associated to each constraint.