A Kantorovich theorem for the structured PSB update in Hilbert space.

DOI10.1023/A:1004666019575zbMath1050.90005OpenAlexW50088619MaRDI QIDQ1584028

M. Laumen

Publication date: 2000

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1004666019575

zbMATH Keywords

Hilbert spaceKantorovich theoremPSB update

Mathematics Subject Classification ID

Programming in abstract spaces (90C48) Optimization of shapes other than minimal surfaces (49Q10) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Computational methods for problems pertaining to operations research and mathematical programming (90-08)

Related Items

The Kantorovich theorem and interior point methods

Cites Work

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• Convergence theory for the structured BFGS secant method with an application to nonlinear least squares
• Application de la méthode des éléments finis à l'approximation d'un problème de domaine optimal. Méthodes de résolution des problèmes approches
• Exploiting additional structure in equality constrained optimization by structured SQP secant algorithms
• Estimation techniques for distributed parameter systems
• A Quasi-Newton Method for Elliptic Boundary Value Problems
• Convergence Theorems for Least-Change Secant Update Methods
• A Sparse Quasi-Newton Update Derived Variationally with a Nondiagonally Weighted Frobenius Norm
• Quasi-Newton Methods and Unconstrained Optimal Control Problems
• On Variable-Metric Methods for Sparse Hessians
• Convergence Results for Schubert’s Method for Solving Sparse Nonlinear Equations
• Local and Superlinear Convergence for Partially Known Quasi-Newton Methods
• A New Proof of Superlinear Convergence for Broyden’s Method in Hilbert Space
• Matrix conditioning and nonlinear optimization
• On Sparse and Symmetric Matrix Updating Subject to a Linear Equation
• On the Use of Product Structure in Secant Methods for Nonlinear Least Squares Problems
• On the Convergence of Broyden's Method for Nonlinear Systems of Equations
• On the Local and Superlinear Convergence of Quasi-Newton Methods
• A Characterization of Superlinear Convergence and Its Application to Quasi-Newton Methods
• An Infinite-Dimensional Convergence Theory for Reduced SQP Methods in Hilbert Space
• Newton's Method for a Class of Optimal Shape Design Problems
• A Class of Methods for Solving Nonlinear Simultaneous Equations
• Modification of a Quasi-Newton Method for Nonlinear Equations with a Sparse Jacobian