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