33,281 research outputs found
Quasiconvex Programming
We define quasiconvex programming, a form of generalized linear programming
in which one seeks the point minimizing the pointwise maximum of a collection
of quasiconvex functions. We survey algorithms for solving quasiconvex programs
either numerically or via generalizations of the dual simplex method from
linear programming, and describe varied applications of this geometric
optimization technique in meshing, scientific computation, information
visualization, automated algorithm analysis, and robust statistics.Comment: 33 pages, 14 figure
Stability of Curvature Measures
We address the problem of curvature estimation from sampled compact sets. The
main contribution is a stability result: we show that the gaussian, mean or
anisotropic curvature measures of the offset of a compact set K with positive
-reach can be estimated by the same curvature measures of the offset of a
compact set K' close to K in the Hausdorff sense. We show how these curvature
measures can be computed for finite unions of balls. The curvature measures of
the offset of a compact set with positive -reach can thus be approximated
by the curvature measures of the offset of a point-cloud sample. These results
can also be interpreted as a framework for an effective and robust notion of
curvature
- …