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Minimizing convex quadratics with variable precision Krylov methods

Serge Gratton(serge.gratton***at***enseeiht.fr)
Ehouarn Simon(ehouarn.simon***at***enseeiht.fr)
Philippe L. Toint(philippe.toint***at***unamur.be)

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.

Keywords: quadratic optimization, multiprecision computations, linear algebra

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Nonlinear Optimization (Quadratic Programming )

Category 3: Optimization Software and Modeling Systems (Other )

Citation: arXiv:1807.07476

Download: [PDF]

Entry Submitted: 07/20/2018
Entry Accepted: 07/20/2018
Entry Last Modified: 07/20/2018

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