Bregman proximal point type algorithms for quasiconvex minimization

Abstract

We discuss a Bregman proximal point type algorithm for dealing with quasiconvex minimization. In particular, we prove that the Bregman proximal point type algorithm converges to a minimal point for the minimization problem of a certain class of quasiconvex functions without neither differentiability nor Lipschitz continuity assumptions, this class of nonconvex functions is known as strongly quasiconvex functions and, as a consequence, we revisited the general case of quasiconvex functions.

Keywords:

• Proximal point algorithms
• Bregman distances
• nonconvex optimization
• generalized convexity
• quasiconvexity

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Anid-Chile [Fondecyt Regular 1220379].