Embedded Files
Quadratic mapping, or quadratic map, is a vector of multivariable functions, each being at most quadratic in its variables. Quadratic maps often appear in various applications as approximations to some non-linear transformations. One frequent question if an image of such a map would be convex. In general this is a difficult question to study. Apparently, if the image is non-convex, the non-convexity must be present at the boundary. It is impossible to have some seemingly convex figure with "bubbles" inside which spoil non-convexity. This is proven in this preprint and illustrated below.
Using this property one can formulate a number of efficient numerical algorithms to probe convexity of the image. We implemented them in a Matlab library which accompanies the paper.
Page updated
Google Sites
Report abuse