ESR12-Arefeh Kavand

I arrived in Birmingham on the 31st of July, and this city had the best first impression on me! :) the weather is nice, with beautiful landscapes and great shopping stores! And the most interesting one is that people drive on the left side of the road here! 😮 So I am cautious while I am crossing the streets! Do You know what I mean? 😁 (first right, then left). Fortunately, I have a colleague here, "Soodeh" ESR 13, who is also Iranian, and from the first day that I arrived here, she has been helping me a lot. Although I can not enter the University of Birmingham (due to COVID-19) and I must work from home, I have regular meetings in-person with Prof. Michal Kocvara and Soodeh. We also had regular zoom meetings with Prof. Michael Stingl (my supervisor at FAU). Almost every day, Soodeh and I work together and can make progress, and it seems this research stay will be very productive.💪  Currently, we are working on two new preconditioners, and we are trying to prove some featu...

I am still working from home, although now we are allowed to go to our office, I prefer to stay home and surprisingly I am completely used to working from home :)) These days I am mostly busy with the process of getting the UK visa, accommodation, and other stuff because I am supposed to go to Birmingham from the first of August and do the rest of my research there in person, I am hoping that everything goes well...😊 I have already started my collaboration with the University of Birmingham (ESR13) "remote" and during this time we (me and ESR13 and the two supervisors) have regular meetings every two weeks and in these meetings, we discuss our progress and the next steps which are really useful and productive for us and I am learning so many new things, also we have made good progress in terms of applying new preconditioners in the SDP problems, and we could successfully run the multiconstraint version of our implementation (PBM) and now we can deal with SDPs with more tha...

Now we are in the position where we have a basic implementation of the PBM (Penalty/Barrier Multiplier method) to deal with solving examples from SDPLIB (with only one constraint). In this implementation, we used   Newton CG  with  a Hessian vector product  with  no preconditioner . Due to the Covid pandemic, working on-site at the university is impossible, so I do home office and weekly zoom meetings with my supervisor. My first research stay at the University of Birmingham (UoB) starts on the 15th of June 2020. So far, the format of this secondment is going to be hybrid, which means half online and half on-site. UoB works on the IPM (Interior Point Methods) for solving SDP problems. Our research has this similarity: we both try our developed algorithm on the same class of problems. Last week we (FAU & UoB) had a zoom meeting. In this meeting, we shared and discussed what has been done, the following steps, and the collaboration structure. For the mome...

Due to the Corona Virus!😓 I have been working at home since the 16th  of March 2020. Nevertheless, all the required facilities for doing Home Office is well prepared by the university, so Alles gut! :) Besides our weekly meeting, which is held every Monday, my supervisor and I discuss implementing the PBM algorithm using online Zoom meetings.  At the moment, the implementation of the PBM algorithm introduced by Zibulevsky and Mosheyev (the paper has been attached in the last post) for solving linear SDPs, is done and could successfully be applied to some examples from SDPLIB. However, there are still some drawbacks to the code regarding efficiency, which is my current task to solve them. Every time we check the code with my supervisor, he recommends some tricks and techniques which are so helpful. I aim to refine the Matlab implementation and prepare it for dealing with polynomial optimization data 💪😁

This week, as my supervisor recommended, I started to read a paper by "Michael Zibulevsky" and "Leonid Mosheyev" on the "Penalty/Barrier Multiplier Algorithm for semidefinite programming." This paper aims to present a generalization of the penalty/Barrier multiplier (PBM) algorithm for SDPs also, a dual analysis of the method based on its correspondence to a proximal point algorithm with a nonquadratic distance-like function has been presented. Also, exploiting the duality of an SDP problem would be practical for many purposes. Therefore, we aim to develop a proper PBM-based algorithm for solving some specific SDP problems.  In general, the SDPS, which comes from polynomial optimization problems, has some difficulties, including the "size" of the problem and "conditioning." Hence some remedies like "CG Newton" for solving the Newton system and developing specific pre-conditioners will be considered. Mosheyev, L., & Michael...

The 1st POEMA workshop in Florence from 15-17 January 2020 was planned to immerse the fresh ESR fellows into our research world, to work up new research ideas into firm plans, and to start weaving professional connections in our research area. Lectures by POEMA scientists and guests were delivered, accompanied by brainstorming challenges and problem sessions. In addition, much time was devoted to open discussions. The courses and talks on the first day of the workshop were "Tensors by Giorgio Ottaviani," "What is Polynomial Optimization by Simone Naldi," and "Decomposition of Tensors and Geometry by Luca Chiantini," In a nutshell, they were mostly about Algebraic concepts and introduction to tensor decomposition and tensor rank, from a geometric point of view, using geometric tools and methods to analyze properties of generic or specific tensors, both in general or in the symmetric case and also a general introduction to polynomial optimization, which is ...

Hello everyone, I am Arefeh (ESR12) my working title of the thesis is “On convex nonlinear semidefinite programming concepts for the solution of p olynomial optimization problems”. I am hosted by the Mathematical Optimization group in the Mathematics Department of the Friedrich-Alexander-University of Erlangen-Nuremberg. The team, led by Michael Stingl, has strong expertise in algorithmic optimization as well as optimization with (partial) differential equations. I am deeply honored that I would be a part of the POEMA from now on. In this weblog, I will be posting  articles describing my research life, my secondment or any topic related to my research in the POEMA. Today is the first day of my working at FAU. I am really really excited about this new chapter of my study life and I am also a little bit stressed out! I have met my supervisor and our team in the mathematics department. the senior researcher of the team, Dr. Fabian Wein, helped me a lot to learn some formaliti...