BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:PGMO Lecture - Peter Buergisser - Optimization\, Invariants\, and 
 Complexity
DTSTART:20250401T080000Z
DTEND:20250403T143000Z
DTSTAMP:20260907T060900Z
UID:indico-event-13504@indico.math.cnrs.fr
DESCRIPTION:Speakers: Quentin Merigot\, Stephane Gaubert (INRIA and Ecole 
 polytechnique)\, Stéphanie CLEVENOT (DEPMAP Polytechnique)\n\n\nIn recent
  years\, a theory of optimization for geodesically convex optimization pro
 blems on Riemannian manifolds has been developed that is adjusted to situa
 tions with high symmetries arising from the action of a typically non-comm
 utative algebraic group. These algorithms minimize the moment map (a versi
 on of the gradient) and test membership to null cones and moment polytopes
  (a vast class of polytopes\, typically of exponential vertex and facet co
 mplexity\, which arise from this a priori non-convex\, non-linear setting)
 .  If the acting groups is commutative (and connected)\, one retrieves th
 e classical setting of geometric programming.\nIn the spirit of standard c
 onvex optimization\, a general first order and a second order method has b
 een developed.  The main technical work goes into identifying the key par
 ameters of the underlying group actions\, which control convergence to the
  optimum in each of these methods. The analysis of these analogues of smoo
 thness parameters relies on from tools from invariant theory.\nThe general
  setting captures a diverse set of problems in different areas of computer
  science\, mathematics\, and physics.  Several of them were solved effici
 ently for the first time using such methods\; the corresponding algorithms
  also led to solutions of purely structural problems and to many new conne
 ctions between disparate fields.  There are intriguing open problems that
  suggest further research directions.\nThe purpose of the course is to pro
 vide an introduction to this new body of work.\n\nhttps://indico.math.cnrs
 .fr/event/13504/
LOCATION:Amphi Becquerel (Tuesday\, Wednesday) and Amphi Carnot (Thursday)
  (Ecole polytechnique)
URL:https://indico.math.cnrs.fr/event/13504/
END:VEVENT
END:VCALENDAR