Quasi-Newton methods in infinite-dimensional spaces and application to matrix equations

DOI10.1007/s10898-010-9564-2zbMath1213.90262OpenAlexW1995117913MaRDI QIDQ628733

Hocine Mokhtar-Kharroubi, Boubakeur Benahmed, Bruno de Malafosse, Adnan Yassine

Publication date: 14 March 2011

Published in: Journal of Global Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10898-010-9564-2

zbMATH Keywords

rate of convergencealgebraic Riccati equationHilbert spacelinear convergencenonlinear equationssuperlinear convergence

Mathematics Subject Classification ID

Methods of quasi-Newton type (90C53) Programming in abstract spaces (90C48)

Related Items (5)

On the implementation of a quasi-Newton interior-point method for PDE-constrained optimization using finite element discretizations ⋮ A new smooth NCP function for solving semidefinite nonlinear complementarity problems ⋮ On the Derivation of Quasi-Newton Formulas for Optimization in Function Spaces ⋮ Local convergence of quasi-Newton methods under metric regularity ⋮ A new inversion-free iterative method for solving a class of nonlinear matrix equations

Uses Software

• Algorithm 432

Cites Work

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• The quasi-Newton method and the infinite matrix theory applied to the continued fractions
• Matrix transformations and quasi-Newton methods
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• A Schur method for solving algebraic Riccati equations
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• A New Proof of Superlinear Convergence for Broyden’s Method in Hilbert Space
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• Newton's Method for Discrete Algebraic Riccati Equations when the Closed-Loop Matrix Has Eigenvalues on the Unit Circle
• A quasi-Newton approach to identification of a parabolic system
• On the Local and Superlinear Convergence of Quasi-Newton Methods
• A Characterization of Superlinear Convergence and Its Application to Quasi-Newton Methods
• A Class of Methods for Solving Nonlinear Simultaneous Equations
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Quasi-Newton Methods and their Application to Function Minimisation
• Davidon’s Method in Hilbert Space
• The Davidon method of solution of the algebraic matrix Riccati equation†
• Davidon’s Method for Minimization Problems in Hilbert Space with an Application to Control Problems

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