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On non-differentiable time-varying optimization

We consider non-differentiable convex optimization problems that vary continuously in time and we propose algorithms that sample these problems at specific time instances and generate a sequence of converging near-optimal decision variables. This sequence converges up to a bounded error to the solution trajectory of the time-varying non-differentiable problems. We illustrate through analytical examples and a realistic numerical simulation the benefit of the algorithms in signal processing applications, e.g., for reconstructing time-varying sparse signals.