Open Access
√(x2 + μ) is the Most Computationally Efficient Smooth Approximation to |x|: a Proof
Carlos Ramirez,Reinaldo Sanchez,Vladik Kreinovich,Miguel Argaez +3 more
- Vol. 8, Iss: 3, pp 205-210
TLDR
In this paper, the authors show that the most computationally efficient smooth approximation to |x| is the function √ x2 + µ, a function which has indeed been successfully used in such optimization.Abstract:
In many practical situations, we need to minimize an expression of the type ∑ |ci|. The problem is that most efficient optimization techniques use the derivative of the objective function, but the function |x| is not differentiable at 0. To make optimization efficient, it is therefore reasonable to approximate |x| by a smooth function. We show that in some reasonable sense, the most computationally efficient smooth approximation to |x| is the function √ x2 + µ, a function which has indeed been successfully used in such optimization. cread more
Citations
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Stable Signal Recovery from Incomplete and Inaccurate Measurements
TL;DR: It is shown that it is possible to recover x0 accurately based on the data y from incomplete and contaminated observations.
Posted Content
Decoding by Linear Programming
Emmanuel J. Candès,Terence Tao +1 more
TL;DR: In this paper, it was shown that under suitable conditions on the coding matrix, the input vector can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program).
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