Convexity of a Small Ball Under Quadratic Map
arXiv:1410.1553 · doi:10.1016/j.laa.2015.09.005
Abstract
We derive an upper bound on the size of a ball such that the image of the ball under quadratic map is strongly convex and smooth. Our result is the best possible improvement of the analogous result by Polyak in the case of quadratic map. We also generalize the notion of the joint numerical range of m-tuple of matrices by adding vector-dependent inhomogeneous terms and provide a sufficient condition for its convexity.
15 pages
References in corpus (1)
Cited by in corpus (5)
- Canonical Universality
- On the Convexity of Image of a Multidimensional Quadratic Map
- Convexity of Solvability Set of Power Distribution Networks
- Some remarks on smooth mappings of Hilbert and Banach spaces and their local convexity property
- An extension of the Polyak convexity principle with application to nonconvex optimization