Journal of Approximation Theory
We discuss the geometric characterization of a subset K of a normed linear space via continuity conditions on the metricprojection onto K. The geometric properties considered includeconvexity, tubularity, and polyhedral structure. The continuityconditions utilized include semicontinuity, generalized stronguniqueness and the non-triviality of the derived mapping. Infinite-dimensional space with the uniform norm we show thatconvexity is equivalent to rotation-invariant almost convexityand we characterize those sets every rotation of which has continuousmetric projection. We show that polyhedral structure underliesgeneralized strong uniqueness of the metric projection.
Original Publication Citation
Huotari, R., & Li, W. (1997). Continuities of metric projection and geometric consequences. Journal of Approximation Theory, 90(3), 319-339. doi:10.1006/jath.1996.3018
Huotari, Robert and Li, Wu, "Continuities of Metric Projection and Geometric Consequences" (1997). Mathematics & Statistics Faculty Publications. 142.