#### Alladi Ramakrishnan Hall

#### Convex Optimization - Random Walks, Localization Lemma and an Isoperimetric Inequality

#### Muthuvel Murugan

##### CMI

*In this talk, we will present a result by Lovasz and Simonovits*

on sampling points uniformly at random random in a convex body. This is

used as a subroutine to solve convex optimization problems. They use a

type of continuous random walk called ball walk to sample points in a

convex body. We will sketch a proof of the convergence of the ball

walk.

We will give a detailed proof of the Lovasz and Simonovits localization

lemma, and a detailed proof an isoperimetric inequality, which is used

in the convergence proof.

Done