Online optimisation studies the convergence of optimisation methods as the data embedded in the problem changes. Based on this idea, we propose a primal dual online method for nonlinear time-discrete inverse problems. We analyse the method through regret theory and demonstrate its performance in real-time monitoring of moving bodies in a fluid with Electrical Impedance Tomography (EIT). To do so, we also prove the second-order differentiability of the Complete Electrode Model (CEM) solution operator on $L^\infty$.

翻译：在线优化研究优化方法在问题中嵌入数据变化时的收敛性。基于这一思想，我们提出了一种针对非线性时间离散反问题的原始对偶在线方法。我们通过遗憾理论分析了该方法，并在电阻抗成像（EIT）中对流体中运动物体的实时监测展示了其性能。为此，我们还证明了完整电极模型（CEM）解算子在$L^\infty$空间上的二阶可微性。