We investigate a family of approximate multi-step proximal point methods, accelerated by implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each update as the proximal point method. We explore several optimization methods where applying an approximate multistep proximal points method results in improved convergence behavior. We argue that this is the result of the lowering of truncation error in approximating gradient flow

翻译：我们研究了一类近似多步近端点方法，通过梯度流的隐式线性离散化进行加速。所得方法为多步近端点方法，每次更新的计算成本与近端点方法相当。我们探索了若干优化方法，其中应用近似多步近端点方法可改善收敛行为。我们认为这是由于在逼近梯度流时截断误差降低所致。