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# Category Archives: Course on Convex Optimization

## 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. … Continue reading

Posted in Course on Convex Optimization, Memos
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## Projected Gradient Descent III — Strong convexity

Strong convexity provides an improved lower bound for a convex function; therefore are in our right to expect the improvement of the rate of convergence of PGD. In this post we will find out how much we actually gain.

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## Projected Gradient Descent I — Lipschitz functions

In this post we find out dimension-free oracle complexity for the following problem class function is -Lipschitz on (with respect to Euclidean norm), i.e. for any is contained in the euclidean ball of radius .

## Black box approach to optimization

To learn convex optimization methods and stack this structure in my head, I decided to write the material down by topics. The focus will be on (constrained) large-scale, or dimension-free, optimization corresponding to first-order methods, with applications to machine learning in mind. I don’t pretend to original contribution … Continue reading

## 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