ESR12-Arefeh Kavand

Finally, after almost two years, we could have another on-site event !😍 I have had the chance to be enrolled in and participate in the  POEMA Learning Week 2  (13th-17th of September, Toulouse-France). It was a great learning and networking opportunity with many informative and entertaining talks and activities. I also could give a talk on " A Primal-Dual Augmented Lagrangian Method for the Solution of Convex Semidefinite Programming Problems with Applications in Structural Optimization  ." In addition, my supervisor "Michael Stingl," gave a Lecture:  On the solution of Semidefinite Programs ," which was an excellent tutorial on the solution of semidefinite programs (SDP), including interior point as well as augmented Lagrangian-type methods. It feels great to see all the partners, including Ph.D. students and supervisors, again in person. We could discuss and share the progress of our research and get the chance to hang out and have so much fun after every s

During these months, we have been primarily working on the idea of Primal-Dual Augmented Lagrangian  (PDAL) , which is inspired by the work of Griva and Polyak in the NLP setting ' Primal-dual nonlinear rescaling method with dynamic scaling parameter update", Mathematical Programming, (2006)'  for the semidefinite programming setting. Based on our numerical observations, Newton's system in the Penalty-Barrier Multipliers/Augmented Lagrangian  (PBM/AL)  approach could not be solved to the required precision, and as a consequence, in the inner iterations, we came up with many iterations without improvement in the value of  dual feasibility  which is the matter of ill-conditioning. By applying the PDAL approach, we avoid solving Newton's system to complete precision, and that is why we expect less trouble with ill-conditioning.  The good news is that we could implement this approach in  Matlab  on three different classes of problems:  selected  SDPLIB  examples (by B.