Minimizing convex quadratics with variable precision Krylov methods

Serge Gratton, Ehouarn Simon, Philippe Toint

Research output: Working paper

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Abstract

Iterative algorithms for the solution of convex quadratic optimization problems are investigated, which exploit inaccurate matrix-vector products. Theoretical bounds on the performance of a Conjugate Gradients and a Full-Orthormalization methods are derived, the necessary quantities occurring in the theoretical bounds estimated and new practical algorithms derived. Numerical experiments suggest that the new methods have significant potential, including in the steadily more important context of multi-precision computations.
Original languageEnglish
PublisherArxiv
Number of pages26
Volume1807.07476
Publication statusSubmitted - 2018

Fingerprint

Krylov Methods
Quadratic Optimization
Cross product
Matrix Product
Conjugate Gradient
Inaccurate
Convex Optimization
Iterative Algorithm
Numerical Experiment
Optimization Problem
Necessary
Experiments
Context

Keywords

  • quadratic optimization
  • multi-precision computing
  • linear algebra

Cite this

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Minimizing convex quadratics with variable precision Krylov methods. / Gratton, Serge; Simon, Ehouarn; Toint, Philippe.

Arxiv, 2018.

Research output: Working paper

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