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SUMMARY:Homotopy methods for convex optimization - Andreas Klingler (Innsb
 ruck)
DTSTART:20240207T143000Z
DTEND:20240207T153000Z
UID:TALK211747@talks.cam.ac.uk
CONTACT:Hamza Fawzi
DESCRIPTION:Convex optimization concerns the problem of finding the maximu
 m of a linear function over a convex set. This class covers many optimizat
 ion problems in quantum information\, portfolio optimization\, and machine
  learning.\n\nIn this talk\, we will introduce a new approach to solving c
 onvex optimization problems via a homotopic approach. In this approach\, w
 e deform an optimization problem with a trivial solution into the target p
 roblem and keep track of the solutions along the homotopy. This is motivat
 ed by the field of numerical algebraic geometry\, which solves systems of 
 polynomial equations using a similar idea.\n\nWe show that our method appl
 ies to certain convex optimization problems\, including Semidefinite Progr
 ams\, Hyperbolic Programs\, and convex optimization problems with a single
  convexity constraint. Moreover\, we present several benchmark problems in
  which this method outperforms known methods.
LOCATION:Centre for Mathematical Sciences MR11\, CMS
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