ESR6-Andries Steenkamp

Today we had a half day but productive one. The speaker  Benoît Legat  lead us through the jungle of code relating to polynomial optimization using Julia before jumping into examples. In particular we did a rather deep dive into  SumOfSquares.jl  a sub package of  JuMP . At first glance there is staggering amount of packages for polynomial in the relatively young language of Julia. Upon some reflection, it is clear why. Just as new cities use the ruins of their predecessors as foundation so too code is written on the failings of previous code. In the case of software the cycle of innovation and improvement is much faster. Keeping up-to-date is hard work. Navigating the jungle of old and new code is no small feat for the new and uninitiated. Fortunately we now have this lecture to guide use a bit in understanding how polynomial optimization fits into the larger Julia/Jump ecosystem. In code, and perhaps math in general it is good to have a minimal viable example ...

To change things up I have decided to make a miniseries on the **POEMA learning week 2** in Toulouse. I do this in contradistinction to the style of the my previous posts. Hence, topics other that mathematics and coding could  be included. With that said and done, welcome to my travel blog. Day zero: 12.09.2021: The calm before the storm. After a lengthy discussion with my colleagues at CWI, it was concluded that the train is the superior form of travel to conferences and the like. Benefiting from leg room, privacy (if you get a cabin) and a smooth ride, trains are the clear choice. In light of this I bought flight tickets because that was the only available option. If like me, you, the reader, made the same mistake and found yourself in a metal cylinder 10 km in the air heading to Toulouse you may also have had the bad judgment choose to take the T1 tram into town after landing. If you did, don't despair. Make it to the terminal station Palais de Justice  and you would be tre...

blog-post Some Julia Language resources. Lately I have been preoccupied with computing lower bounds for the completely positive matrix factorization rank of a suitable matrix A. Though, this post is not about the mathematics of this topic rather than the software that I am using, namely Julia Language. To quote from Wikipedia : Julia is a high-level, high-performance, dynamic programming language. While it is a general-purpose language and can be used to write any application, many of its features are well suited for numerical analysis and computational science. It is my hope that in this post I can share some of the resources and study material that I found and thereby save the reader time and effort in learning Julia Language. I am by no means an expert in this topic but the links I provide should help the reader find his/her way to experts. Some notes: Julia is fast, click here to see how the ...

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 ...