Linear convergence of accelerated conditional gradient algorithms in spaces of measures

Understand

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.