My second research stay at NAG (Oxford-UK)

  My secondment in NAG took place online in November-December 2021 in collaboration with Jan Fiala and Shuanghua Bai. As an introduction, NAG provides industry-leading numerical software and technical services to banking and finance, energy, engineering, and market research, as well as academic and government institutions. NAG also offers Automatic Differentiation, Machine Learning, and Mathematical Optimization products, as well as world-class technical consultancy across HPC and Cloud HPC, code porting and optimization, and other areas of numerical computing. Founded over 50 years ago from a multi-university venture, NAG is headquartered in Oxford, UK, with offices in the UK, US, EU, and Asia. At FAU (my host university), my supervisor (Prof. Michael Stingl) and I could design a Primal-Dual Penalty/Barrier Multiplier Augmented Lagrangian (PBM-AL) algorithm for the solution of Semidefinite Programs (SDP), the efficiency of the overall algorithm is demonstrated by numerical experiments for different class of SDPs, including examples from SDPLIB, medium to significant graph problems as well as truss topology optimization problems. The purpose of this secondment was to computationally study and explore how to effectively solve a particular class of SDP problems, including SDP relaxations coming from optimal power flow (OPF) problems, by using our developed algorithm at FAU. The classical OPF problem is a nonconvex NLP.

On the other hand, the SDP belongs to convex optimization and can guarantee optimal global solutions using a desired algorithm. Hence, it is worth studying how to correctly reformulate the classical OPF to an SDP model and benefits from the SDP techniques. Related literature, as well as a package called "MATPOWER"-an open source Matlab-language M-files for solving steady-state power system simulation and optimization problems such as power flow 3 - has been introduced by NAG, as it was a new subject for me in our weekly online meetings with Shuanghau Bai, we mainly discussed on the structure and modeling of the SDP relaxation for these specific problems. In this open-source MATPOWER package, another software package for optimization modeling tool YALMIP and a semidefinite programming solver compatible with YALMIP, such as SEDUMI or SDPT3, are required. The plan was to make the required changes in modeling OPF problems in order to be able to plug in the Primal-Dual PBM-AL solver instead of so-called solvers, so I was mainly focusing on both solvers to see how our algorithm could work efficiently or if it could be improved for these specific problems. As the duration of this secondment needed to be increased for this goal, it is an ongoing collaboration and still needs more time for the numerical results to be finalized.

          Newsletter April 2022.pdf - Google Drive 





 

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