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  • The limiting factors of second-order methods for large-scale semidefinite optimization are the storage and factorization of the Newton matrix. For a particular algorithm based on the modified barrier method, we propose to use iterative solvers instead of the routinely used direct factorization techniques. The preconditioned conjugate gradient method proves to be a viable alternative for problems with a large number of variables and modest size of the constrained matrix. We further propose to avoid explicit calculation of the Newton matrix either by an implicit scheme in the matrix-vector product or using a finite-difference formula. This leads to huge savings in memory requirements and, for certain problems, to further speed-up of the algorithm.
  • The limiting factors of second-order methods for large-scale semidefinite optimization are the storage and factorization of the Newton matrix. For a particular algorithm based on the modified barrier method, we propose to use iterative solvers instead of the routinely used direct factorization techniques. The preconditioned conjugate gradient method proves to be a viable alternative for problems with a large number of variables and modest size of the constrained matrix. We further propose to avoid explicit calculation of the Newton matrix either by an implicit scheme in the matrix-vector product or using a finite-difference formula. This leads to huge savings in memory requirements and, for certain problems, to further speed-up of the algorithm. (en)
  • Limitováné faktorý druhotných metod pro rozsáhlé semidifinitní optimalizace jsou uložené a faktorizovány v Newtonově matici. Pro praktický algoritmus založený na modifikované metodě bariér jsme nuceni použít iterativních výpočetních zařítení, používaných pro přímé faktorizování techniky. (cs)
Title
  • On the solution of large-scale SDP problems by the modified barrier method using iterative solvers
  • On the solution of large-scale SDP problems by the modified barrier method using iterative solvers (en)
  • Řešení rozsáhlých SDP problémů modifikovanou metodou bariér za použití iterativních výpočetních zařízení (cs)
skos:prefLabel
  • On the solution of large-scale SDP problems by the modified barrier method using iterative solvers
  • On the solution of large-scale SDP problems by the modified barrier method using iterative solvers (en)
  • Řešení rozsáhlých SDP problémů modifikovanou metodou bariér za použití iterativních výpočetních zařízení (cs)
skos:notation
  • RIV/67985556:_____/07:00322640!RIV09-AV0-67985556
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(IAA1075402), Z(AV0Z10750506)
http://linked.open...iv/cisloPeriodika
  • 2-3
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 439434
http://linked.open...ai/riv/idVysledku
  • RIV/67985556:_____/07:00322640
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • semidefinite programming; iterative methods; preconditioned conjugate gradients; augmented lagrangian methods (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • NL - Nizozemsko
http://linked.open...ontrolniKodProRIV
  • [24AEB5CCC8B5]
http://linked.open...i/riv/nazevZdroje
  • Mathematical Programming
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 109
http://linked.open...iv/tvurceVysledku
  • Kočvara, Michal
  • Stingl, M.
http://linked.open...ain/vavai/riv/wos
  • 000243908500010
http://linked.open...n/vavai/riv/zamer
issn
  • 0025-5610
number of pages
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