Preconditioner?...Collaboration with ESR13

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 moment, we are going to work on a paper (attached to this post), and we should implement a special preconditioner that suits our approach. Currently, I am modifying our developed Matlab code to deal with SDP problems with more than one LMI constraint.


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