# Linear convergence of accelerated conditional gradient algorithms in spaces of measures

arXiv: https://arxiv.org/abs/1904.09218 · HTML: https://mlsanity.com/paper/1904.09218/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2019.

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## Abstract (arXiv)

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 O(1/k) 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 O(zetak) convergence rate is obtained locally.