Convexity of a small ball under quadratic map

Anatoly Dymarsky

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 [1] in the case of a quadratic map. We also generalize the notion of the joint numerical range of m-tuple of matrices by adding vector-dependent inhomogeneous term and provide a sufficient condition for its convexity.

Original languageEnglish
Article number13356
Pages (from-to)109-123
Number of pages15
JournalLinear Algebra and Its Applications
Publication statusPublished - 1 Jan 2016


  • Convexity
  • Joint numerical range
  • Quadratic transformation (map)
  • Trust region problem


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