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# Category Archives: Memos

## Thresholding over the l1-ball

Since long ago I wanted to write a post with an elementary introduction to soft / hard thresholding. The time has come to pay the dues, so here we go.

Posted in Memos, Sparsity, Statistics
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## Formulations of Mirror Descent

A very nice reference for this post is [this blog post]. Mirror Descent is a first-order algorithm to solve a convex optimization problem In this post we will learn several equivalent formulations of this algorithm and discuss how they are related to each other.

Posted in Course on Convex Optimization, Memos
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## Brunn-Minkowski, Prékopa-Leindler, and isoperimetry

Found a great overview of the subject with a lot of insight. Another brief intro is here.

## Fourier transforms

Here is a recap of proper normalizations for the Fourier series/DTFT (i.e. torus/ domains), DFT (), and also a brief reminder of Plancherel’s theorem.

## Projection on a convex set is closer to any point of the set

A useful little fact for constrained optimization. Let be a convex set, and consider and its projection on As quickly follows from the separation theorem with hyperplane containing for any the angle between and is obtuse. … Continue reading

Posted in Convex Optimization, Course on Convex Optimization, Memos
Tagged convex geometry
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## Sandwiching smooth convex functions

If a function has a Lipschitz gradient, i.e. for any and then

## Farkas’ lemma

Farkas’ lemma is a simple (and very useful) statement in convex analysis. Theorem (Farkas’ lemma) For any matrix and vector , exactly one of the following holds: (1) linear system has a solution in the first … Continue reading

Posted in Convex Optimization, Memos, Optimization tricks
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