Linear convergence of accelerated conditional gradient algorithms in spaces of measures

Abstract

A class of generalized conditional gradient algorithms for the solution of optimization problem in spaces of Radon measures is presented. The method iteratively inserts additional Dirac-delta functions and optimizes the corresponding coefficients. Under general assumptions, a sub-linear [see formula in PDF] rate in the objective functional is obtained, which is sharp in most cases. To improve efficiency, one can fully resolve the finite-dimensional subproblems occurring in each iteration of the method. We provide an analysis for the resulting procedure: under a structural assumption on the optimal solution, a linear [see formula in PDF] convergence rate is obtained locally.

Document Details

Document Type
Pub Defense Publication
Publication Date
Jan 01, 2021
Source ID
10.1051/cocv/2021042

Entities

People

  • Daniel Walter
  • Konstantin Pieper

Organizations

  • Air Force Office of Scientific Research
  • Elite Network of Bavaria
  • German Research Foundation
  • Technical University of Munich
  • United States Department of Energy

Tags

Fields of Study

  • Mathematics

Readers

  • Distributed Systems and Data Platform Development
  • Plasma Physics / Magnetohydrodynamics
  • Statistical inference.

Technology Areas

  • Space