On the Polyak convexity principle and its application to variational analysis

@inproceedings{Uderzo2013OnTP,
  title={On the Polyak convexity principle and its application to variational analysis},
  author={A. Uderzo},
  year={2013}
}
According to a result due to B.T. Polyak, a mapping between Hilbert spaces, which is $C^{1,1}$ around a regular point, carries a ball centered at that point to a convex set, provided that the radius of the ball is small enough. The present paper considers the extension of such result to mappings defined on a certain subclass of uniformly convex Banach spaces. This enables one to extend to such setting a variational principle for constrained optimization problems, already observed in finite… CONTINUE READING