Minimizing convex quadratics with variable precision Krylov methods

Serge Gratton; Ehouarn Simon; Philippe Toint

Minimizing convex quadratics with variable precision Krylov methods

Serge Gratton, Ehouarn Simon, Philippe Toint

Namur Institute for Complex Systems

Research output: Contribution to journal › Article › peer-review

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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 language	English
Pages (from-to)	e2337
Number of pages	26
Journal	Numerical Linear Algebra with Applications
Volume	28
Issue number	1
Publication status	Published - 1 Oct 2020

Keywords

quadratic optimization
multi-precision computing
linear algebra

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2020_TointP_articleSubmitted manuscript, 417 KBLicence: Unspecified

2 Article

A note on solving nonlinear optimization problems in variable precision
Gratton, S. & Toint, P. L., 1 Jul 2020, In: Computational Optimization and Applications. 76, 3, p. 917-933 17 p.
Research output: Contribution to journal › Article › peer-review

Open Access
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Range-space variants and inexact matrix-vector products in Krylov solvers for linear systems arising from inverse problems
Gratton, S., Toint, P. & Tshimanga Ilunga, J., 1 Jan 2011, In: SIAM Journal on Matrix Analysis and Applications. 32, 3, p. 969-986 18 p.
Research output: Contribution to journal › Article › peer-review

File
57 Downloads (Pure)

3 Invited talk
1 Visiting an external academic institution

ENSEEIHT-IRIT
Philippe Toint (Visiting researcher)
4 Nov 2019 → 8 Nov 2019
Activity: Visiting an external institution types › Visiting an external academic institution
Minimizing convex quadratics with variable precision Krylov methods
Philippe Toint (Speaker)
28 Nov 2019
Activity: Talk or presentation types › Invited talk
Minimizing convex quadratics with variable precision Krylov methods
Philippe Toint (Speaker)
10 Oct 2019
Activity: Talk or presentation types › Invited talk

Cite this

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title = "Minimizing convex quadratics with variable precision Krylov methods",

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.",

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AB - 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.

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KW - multi-precision computing

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JF - Numerical Linear Algebra with Applications

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ER -

Minimizing convex quadratics with variable precision Krylov methods

Abstract

Keywords

Access to Document

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Research output

A note on solving nonlinear optimization problems in variable precision

Range-space variants and inexact matrix-vector products in Krylov solvers for linear systems arising from inverse problems

Activities

ENSEEIHT-IRIT