publication . Article . Preprint . 2015

Dictionary descent in optimization

Temlyakov, Vladimir;
Open Access
  • Published: 04 Nov 2015 Journal: Analysis Mathematica, volume 42, pages 69-89 (issn: 0133-3852, eissn: 1588-273X, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
The problem of convex optimization is studied. Usually in convex optimization the minimization is over a d-dimensional domain. Very often the convergence rate of an optimization algorithm depends on the dimension d. The algorithms studied in this paper utilize dictionaries instead of a canonical basis used in the coordinate descent algorithms. We show how this approach allows us to reduce dimensionality of the problem. Also, we investigate which properties of a dictionary are beneficial for the convergence rate of typical greedy-type algorithms.
free text keywords: General Mathematics, Standard basis, Coordinate descent, Rate of convergence, Banach space, Optimization algorithm, Convex optimization, Mathematics, Curse of dimensionality, Topology, Minification, Mathematical optimization, Statistics - Machine Learning, Mathematics - Numerical Analysis
Related Organizations
Funded by
NSF| Greedy Approximation in Banach Spaces and Compressed Sensing
  • Funder: National Science Foundation (NSF)
  • Project Code: 1160841
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
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publication . Article . Preprint . 2015

Dictionary descent in optimization

Temlyakov, Vladimir;