Consider a polynomial optimisation problem, whose instances vary continuouslyover time. We propose to use a coordinate-descent algorithm for solving suchtime-varying optimisation problems. In particular, we focus on relaxations oftransmission-constrained problems in power systems. On the example of the alternating-current optimal power flows (ACOPF), webound the difference between the current approximate optimal cost generated byour algorithm and the optimal cost for a relaxation using the most recent datafrom above by a function of the properties of the instance and the rate ofchange to the instance over time. We also bound the number of floating-pointoperations that need to be performed between two updates in order to guaranteethe error is bounded from above by a given constant.
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