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SUMMARY:Volkan Cevher (EPFL)
DTSTART:20200608T130000Z
DTEND:20200608T140000Z
DTSTAMP:20260423T021004Z
UID:OWOS/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWOS/10/">Sc
 alable semidefinite programming</a>\nby Volkan Cevher (EPFL) as part of On
 e World Optimization seminar\n\n\nAbstract\nThis talk first introduces new
  convex optimization methods based on linear minimization oracles to obtai
 n numerical solutions to semidefinite programs with a low-rank matrix stre
 aming model. This streaming model provides us an opportunity to integrate\
 nsketching as a new tool for developing storage optimal convex optimizatio
 n methods that can solve semidefinite programs (SDP) efficiently within sp
 ace required to write down the problem and its solution.\n\nIn particular\
 , for SDP formulations\, we obtain an approximate solution within an $\\ep
 silon$-error region in the objective residual and distance to feasible set
 \, after a total of $\\texttt{Const}\\cdot \\epsilon^{-5/2}\\log(n/\\epsil
 on)$ matrix vector multiplications for the linear minimization oracle (app
 roximate eigenvalue calculation)\, and an additional $\\mathcal{O}(\\max(n
 \,d)/\\epsilon^2)$ arithmetic operations for the remaining arithmetics. $\
 \texttt{Const}$ is problem independent.\n\nWe then discuss a practical ine
 xact augmented Lagrangian method for non-convex problems with nonlinear co
 nstraints and contrast this approach to the convex one for solving SDPs. W
 e characterize the total computational complexity of the non-convex method
  subject to a verifiable geometric condition\, followed by numerical demon
 strations that include\, max-cut\, unsupervised clustering\, and quadratic
  assignment problems. \n\nThe talk is based on joint work with several col
 laborators\, including Alp Yurtsever\, Olivier Fercoq\, Joel A. Tropp\, Ma
 deleine Udell\, Fatih Sahin\, Armin Eftekhari\, and Ahmet Alacaoglu.\n\nth
 e address and password of the zoom room of the seminar are sent by e-mail 
 on the mailinglist of the seminar one day before each talk\n
LOCATION:https://researchseminars.org/talk/OWOS/10/
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