| Autor: |
Trautmann, Philip, Walter, Daniel |
| Rok vydání: |
2021 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We analyze a solution method for minimization problems over a space of $\mathbb{R}^d$-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 $\mathcal{O}(1/k)$ 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 $\mathcal{O}(\zeta^k)$ for some $\zeta <1$. Moreover, in this case, the same rate can be expected for the iterates in $L^1(I;\mathbb{R}^d)$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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