A brief touch on term sparsity

Comments

Post a Comment

Popular posts from this blog

POEMA learning week 2: Day 2

Image
Today was a full day. Starting with a triple whammy of POEMA ESR talks we got off to a running start. I will try my best to recall the highlights (based on my own limited understanding and memory) of the day: ESR2 Andrew  : Attacking polynomial optimization problems via the critical values route. This means computing the Jacobian of the system and then solving a determental system using a very subject specific algorithm Sparse FGLM algorithm . ESR4 Alejandro  : A verbose intro into real zero (RZ) polynomials from theory down to numerics. I had hoped to see a clearer link between RZ polynomials and the Generalized Lax Conjecture but hey-ho. ESR12 Arefeh : Leveraging both primal and dual formulations in solving SDP's. Also extensions to sparse large SDP's and preconditioners for low rank SDPs. Considering how much I rely on SDP solvers I am painfully unaware of all the intricacies of their operation. I am glad Arefeh is an expert I can refer to should the need arise. Prof. Dr. T...
Read more

Some Julia Language resources

Image
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 ...
Read more

POEMA learning week 2: Day 1

Image
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 ...
Read more