Central Curve in Semidefinite Programming

Algebra Seminar
Monday, February 6, 2023 - 10:20am for 1.5 hours (actually 80 minutes)
Skiles 005
Isabelle Shankar – Portland State University – isabelle.shankar@pdx.eduhttps://sites.google.com/view/isabelle-shankar
Abeer Al Ahmadieh

The Zariski closure of the central path (which interior point algorithms track in convex optimization problems such as linear and semidefinite programs) is an algebraic curve, called the central curve. Its degree has been studied in relation to the complexity of these interior point algorithms.  We show that the degree of the central curve for generic semidefinite programs is equal to the maximum likelihood degree of linear concentration models.  This is joint work with Serkan Hoşten and Angélica Torres.