A brief touch on term sparsity

Comments

Post a Comment

Popular posts from this blog

Purpose of this blog: To log my mathematical endeavours.

Why does this blog exist? I am required to maintain a blog of my research activities as mandated by my contract with POEMA. Secondly this blog will serve as record for evaluating my progress (both for me and my superiors) as well as a platform to showcase my interests (to possible collaborators). Thirdly, it serve as a source of information to anyone interested in me or the topics I study. I must warn the reader that I am a novice to the practice of blogging. Hence, constructive criticism is welcomed. What is the content of this blog? In this blog I will record my mathematical endeavours, indexed by the week in which they take place. The mathematical endeavours are directed towards the topic of :  Approximation hierarchies for (non-)commutative polynomial optimisation. This topic falls under general polynomial optimisation techniques and is know to use tools from (but not limited to): real algebra moment theory operator theory semidefinite optimisation. In addition ...
Read more

A way to approximate the volume of semi algebraic sets using SDPs

Image
On Wednesday 30.01.2020 as part of a reading group I presented the work of: D. Henrion, J. B. Lasserre and C. Savorgnan on: Approximate Volume and Integration for Basic Semi-algebraic Sets. [ https://doi.org/10.1137/080730287 ] I wish to share some interesting bits of knowledge I came across. It is not my intention to fully and rigorously reproduce the contents of the above mentioned paper. Hence, if you are interested in the topic mentioned then please consult the paper. I was suggested this paper by Monique because it shows two things. The first being that finding the volume of a compact  basic semi-algebraic set K that is Archemedean (on the polynomials g_i defining  K), can be recast as a minimisation problem over measures (see Theorem 3.1). The  second thing that is shown is that this problem can be approximated by a hierarchy of SDP approximations that return the moments of a minimising measure. Both of these topics fall well within the scope of ...
Read more