Events

MATH Dept. - Special Seminar by the Distinguished Visitor - Prof. Boris Mordukhovich

Convergence of Descent Optimization  Algorithms Under Polyak- Lojasiewicz-Kurdyka Conditions
 
Date: Monday, February 17, 2025
Time:  10:00 AM
Location: Building 5, Room 103

 

Speaker:

Prof. Boris Mordukhovich
Department of Mathematics,
Wayne State University
USA.

 

 Abstract:

This paper develops the novel convergence analysis of a generic class of descent methods in nonsmooth and nonconvex optimization under several versions of the Polyak- Lojasiewicz -Kurdyka (PLK) properties. Along with other results, we prove the finite termination of generic algorithms under the PL K property with lower exponents. Specifications are given to convergence rates of some particular algorithms including inexact reduced gradient methods and the boosted algorithm in DC programming. It is revealed, e.g., that the lower exponent PLK property in the DC framework is incompatible with the gradient Lipschitz continuity for the plus function around a local minimizer. On the other hand, we show that the above inconsistency observation may fail if the Lipschitz continuity is replaced by merely the gradient continuity.

 
Based on joint work with G. Bento, T. Mota and Yu. Nesterov.
 
 
All are cordially invited to attend.

    Location
  • Building 5, Room 103

  • 17 Feb, 2025

  • 10:00 AM - 12:00 PM