
Chebushev Greedy Algorithm in convex optimization
Chebyshev Greedy Algorithm is a generalization of the well known Orthogo...
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On optimal convergence rates of spectral orthogonal projection approximation for functions of algbraic and logarithmatic regularities
Based on the Hilb type formula between Jacobi polynomials and Bessel fun...
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Convergence rates of spectral orthogonal projection approximation for functions of algebraic and logarithmatic regularities
Based on the Hilb type formula between Jacobi polynomials and Bessel fun...
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Convergence and rate of convergence of some greedy algorithms in convex optimization
The paper gives a systematic study of the approximate versions of three ...
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Dictionary descent in optimization
The problem of convex optimization is studied. Usually in convex optimiz...
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Optimal Construction for TimeConvex Hull with Two Orthogonal Highways in the L1metric
We consider the timeconvex hull problem in the presence of two orthogon...
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Sparse Optimization on General Atomic Sets: Greedy and ForwardBackward Algorithms
We consider the problem of sparse atomic optimization, where the notion ...
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Improved Convergence Rates for the Orthogonal Greedy Algorithm
We analyze the orthogonal greedy algorithm when applied to dictionaries 𝔻 whose convex hull has small entropy. We show that if the metric entropy of the convex hull of 𝔻 decays at a rate of O(n^1/2α) for α > 0, then the orthogonal greedy algorithm converges at the same rate. This improves upon the wellknown O(n^1/2) convergence rate of the orthogonal greedy algorithm in many cases, most notably for dictionaries corresponding to shallow neural networks. Finally, we show that these improved rates are sharp under the given entropy decay assumptions.
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