Abstract
We analyse a solution method for minimization problems over a space of -valued functions of bounded variation on an interval I. The presented method relies on piecewise constant iterates. In each iteration, the algorithm alternates between proposing a new point at which the iterate is allowed to be discontinuous and optimizing the magnitude of its jumps as well as the offset. A sublinear convergence rate for the objective function values is obtained in general settings. Under additional structural assumptions on the dual variable, this can be improved to a locally linear rate of convergence for some . Moreover, in this case, the same rate can be expected for the iterates in .
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