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On the solution of large-scale SDP problems by the modified barrier method using iterative solvers

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    0322640 - ÚTIA 2009 RIV NL eng J - Journal Article
    Kočvara, Michal - Stingl, M.
    On the solution of large-scale SDP problems by the modified barrier method using iterative solvers.
    [Řešení rozsáhlých SDP problémů modifikovanou metodou bariér za použití iterativních výpočetních zařízení.]
    Mathematical Programming. Roč. 109, 2-3 (2007), s. 413-444. ISSN 0025-5610. E-ISSN 1436-4646
    R&D Projects: GA AV ČR IAA1075402
    Institutional research plan: CEZ:AV0Z10750506
    Keywords : semidefinite programming * iterative methods * preconditioned conjugate gradients * augmented lagrangian methods
    Subject RIV: BA - General Mathematics
    Impact factor: 1.475, year: 2007

    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.

    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.
    Permanent Link: http://hdl.handle.net/11104/0170830

     
     
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