Spectral analysis of block preconditioners for double saddle-point linear systems with application to PDE-constrained optimization

Luca Bergamaschi (), Ángeles Martínez (), John W. Pearson () and Andreas Potschka ()
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Luca Bergamaschi: University of Padua
Ángeles Martínez: University of Trieste
John W. Pearson: The University of Edinburgh
Andreas Potschka: Clausthal University of Technology

Computational Optimization and Applications, 2025, vol. 91, issue 2, No 4, 423-455

Abstract: Abstract In this paper, we describe and analyze the spectral properties of a symmetric positive definite inexact block preconditioner for a class of symmetric, double saddle-point linear systems. We develop a spectral analysis of the preconditioned matrix, showing that its eigenvalues can be described in terms of the roots of a cubic polynomial with real coefficients. We illustrate the efficiency of the proposed preconditioners, and verify the theoretical bounds, in solving large-scale PDE-constrained optimization problems.

Keywords: Double saddle-point problems; Preconditioning; Krylov subspace methods; PDE-constrained optimization.; 65F08; 65F10; 65F50; 49M41 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10589-024-00623-2

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