ACDS
swMATH ID:  31742 
Software Authors:  Vorontsova, E. A.; Gasnikov, A. V.; Gorbunov, E. A. 
Description:  Accelerated directional search with nonEuclidean proxstructure. We consider smooth convex optimization problems whose full gradient is not available for their numerical solution. In 2011, Yu.E. Nesterov proposed accelerated gradientfree methods for solving such problems. Since only unconditional optimization problems were considered, Euclidean proxstructures were used. However, if one knows in advance, say, that the solution to the problem is sparse, or rather that the distance from the starting point to the solution in 1norm and in 2norm are close, then it is more advantageous to choose a nonEuclidean proxstructure associated with the 1norm rather than a proxstructure associated with the 1norm. In this work we present a complete justification of this statement. We propose an accelerated descent method along a random direction with a nonEuclidean proxstructure for solving unconditional optimization problems (in further work, we propose to extend this approach to an accelerated gradientfree method). We obtain estimates of the rate of convergence for the method and show the difficulties of transferring the abovementioned approach to conditional optimization problems. 
Homepage:  https://arxiv.org/abs/1710.00162 
Source Code:  https://github.com/evorontsova/ACDF 
Keywords:  firstorder accelerated methods; convex optimization; linear coupling method; uniform measure concentration on single euclidean sphere; nonEuclidean proxstructure 
Related Software:  GitHub; BRENT; DiffSharp 
Cited in:  3 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

Accelerated directional search with nonEuclidean proxstructure. Zbl 1434.90143 Vorontsova, E. A.; Gasnikov, A. V.; Gorbunov, E. A. 
2019

Cited by 4 Authors
3  Gasnikov, Alexander V. 
3  Gorbunov, E. A. 
3  Vorontsova, Evgeniya Alexeevna 
1  Dvurechensky, Pavel E. 
Cited in 2 Serials
2  Automation and Remote Control 
1  Mathematical Notes 
Cited in 3 Fields
2  Operations research, mathematical programming (90XX) 
1  Calculus of variations and optimal control; optimization (49XX) 
1  Probability theory and stochastic processes (60XX) 