Linear convergence of accelerated conditional gradient algorithms in spaces of measures

Konstantin Pieper; Daniel Walter

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arXiv · 1904.09218

Linear convergence of accelerated conditional gradient algorithms in spaces of measures

Konstantin Pieper·Daniel Walter

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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 $\mathcal{O}(1/k)$ 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 $\mathcal{O}(\zeta^k)$ convergence rate is obtained locally.

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Konstantin Pieper, Daniel Walter. 2019-04-19. Linear convergence of accelerated conditional gradient algorithms in spaces of measures. https://arxiv.org/abs/1904.09218

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