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SUMMARY:Exploiting Sparsity in Semidefinite and Sum of Squares Programming
  - Antonis Papachristodoulou\, University of Oxford
DTSTART:20200220T140000Z
DTEND:20200220T150000Z
UID:TALK132418@talks.cam.ac.uk
CONTACT:Alberto Padoan
DESCRIPTION:Semidefinite and sum of squares optimization have found a wide
  range of applications\, including control theory\, fluid dynamics\, machi
 ne learning\, and power systems. In theory they can be solved in polynomia
 l time using interior-point methods. However\, these methods are only prac
 tical for small- to medium- sized problem instances.\n\nFor large instance
 s\, it is essential to exploit or even impose sparsity and structure withi
 n the problem in order to solve the associated programs efficiently. In th
 is talk I will present recent results on the analysis and design of networ
 ked systems\, where chordal sparsity can be used to decompose the resultin
 g SDPs\, and solve an equivalent set of smaller semidefinite constraints. 
 I will also discuss how sparsity and operator-splitting methods can be use
 d to speed up computation of large SDPs and introduce our open-source solv
 er CDCS. Lastly\, I will extend the decomposition result on SDPs to SOS op
 timization with polynomial constraints\, revealing a practical way to conn
 ect SOS optimization and DSOS/SDSOS optimization for sparse problem instan
 ces.\n
LOCATION:Cambridge University Engineering Department\, Seminar Room JDB
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