Foundations of Computational Mathematics

, Volume 16, Issue 2, pp 369–394

Convex Optimization on Banach Spaces

Article

DOI: 10.1007/s10208-015-9248-x

Cite this article as:
DeVore, R.A. & Temlyakov, V.N. Found Comput Math (2016) 16: 369. doi:10.1007/s10208-015-9248-x

Abstract

Greedy algorithms which use only function evaluations are applied to convex optimization in a general Banach space \(X\). Along with algorithms that use exact evaluations, algorithms with approximate evaluations are treated. A priori upper bounds for the convergence rate of the proposed algorithms are given. These bounds depend on the smoothness of the objective function and the sparsity or compressibility (with respect to a given dictionary) of a point in \(X\) where the minimum is attained.

Keywords

Sparse Optimization Greedy Banach space  Convergence rate Approximate evaluation 

Mathematics Subject Classification

Primary: 41A46 Secondary: 65K05 41A65 46B20 

Copyright information

© SFoCM 2015

Authors and Affiliations

  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA
  2. 2.Department of MathematicsUniversity of South CarolinaColumbiaUSA