# Convex Optimization on Banach Spaces

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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

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## 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

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