Papers › Accelerated Directional Search with non-Euclidean prox-structure
Accelerated Directional Search with non-Euclidean prox-structure
Evgeniya Vorontsova, Alexander Gasnikov, Eduard Gorbunov
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In the paper we propose an accelerated directional search method with non-euclidian prox-structure. We consider convex unconstraint optimization problem in ℝⁿ. For simplicity we start from the zero point. We expect in advance that 1-norm of the solution is close enough to its 2-norm. In this case the standard accelerated Nesterov's directional search method can be improved. In the paper we show how to make Nesterov's method n-times faster (up to a logn-factor) in this case. The basic idea is to use linear coupling, proposed by Allen-Zhu & Orecchia in 2014, and to make Grad-step in 2-norm, but Mirr-step in 1-norm. We show that for constrained optimization problems this approach stable upon an obstacle.
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