Convex valued geodesics and applications to sweeping processes with bounded retraction

具有有界回缩的近端正则扫掠过程

Prox-regular sweeping processes with bounded retraction

本文证明了一致近端正则运动集驱动的 Moreau 扫掠过程在局部有界回缩条件下解的唯一性，并通过重参数化技术将该情形归结为可借助追赶算法求解的 Lipschitz 连续情形。

Newton retraction as approximate geodesics on submanifolds

Efficient approximation of geodesics is crucial for practical algorithms on manifolds. Here we introduce a class of retractions on submanifolds, induced by a foliation of the ambient manifold. They match the projective retraction to the third order and thus match the exponential map to the second order. In particular, we show that Newton retraction (NR) is always stabler than the popular approach known as oblique projection or orthographic retraction: per Kantorovich-type convergence theorems, the superlinear convergence regions of NR include those of the latter. We also show that NR always ha…