Soodeh Habibi, an ESR of University of Birmingham has had 3 months secondments with Inria, France. The purpose of the secondment is to use SDP solver Loraine for moment tools and test it on low-rank SDP problems coming from Geometry like intersecting curves, algebraic curves, and Geometric modeling. These problems can be constrained to some optimization problems with a finite set of solutions. She was also looking at the Robotic Problems.
In this secondment, Soodeh and the team worked on the connection between Julia and MATLAB and how they can use SDP solver Loraine for moment tools. Now, they can call Loraine directly from Julia and solve the SDP problem coming from the moment tools that fulfill our assumptions. They are using moment tools and building relaxation in some order. In this relaxation, there are SDP matrices that can be given to Loraine.
In addition, and majorly, they looked at the formulation of different problems as polynomial optimization and solved them using relaxation. These problems include self-Intersection (SI), surface-surface intersection (SSI), minimum volume sphere, minimum enclosing ellipsoid (MEE), and minimum bounding box (MBB). They applied these problems to different geometric models like teapot and robot problems. One of the new approaches is to the MEE problem. This problem finds the ellipsoid of the smallest volume that fully contains a polynomial patch. There is already some research about finding this ellipsoid when the center point is defined (center at the origin). They did the modeling for the ellipsoid when the center point is not defined, and it is a free variable. Theyare use problems of computed quadratic modules or sum of squares (SOS). This leads to a convex optimization problem in which the solution results in the minimum ellipsoid.
