近端光滑集的可求长曲线
Rectifiable curves in proximally smooth sets
摘要：
在一致凸、一致光滑的巴拿赫空间中，给出了在邻近光滑集的两个充分近点之间构造一条可求长曲线的算法.我们的算法返回一个合理的短曲线之间的两个足够接近的点的近端光滑集，是迭代的，并使用一定的修改的度量投影。我们估计构造曲线的长度及其与具有相同端点的线段的偏差。这些估计与希尔伯特空间中近似光滑集上的测地线的估计在一个常数因子上一致。
英文摘要：
We provide an algorithm of constructing a rectifiable curve between two sufficiently close points of a proximally smooth set in a uniformly convex and uniformly smooth Banach space. Our algorithm returns a reasonably short curve between two sufficiently close points of a proximally smooth set, is iterative and uses a certain modification of the metric projection. We estimate the length of a constructed curve and its deviation from the segment with the same endpoints. These estimates coincide up to a constant factor with those for the geodesics in a proximally smooth set in a Hilbert space.
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