Numerical solution of KKT systems in PDE-constrained optimization problems via the affine scaling trust-region approach†

DOI10.1080/00207160802155294zbMath1181.65093OpenAlexW2089705764MaRDI QIDQ5850761

Sandra Pieraccini, Stefania Bellavia

Publication date: 15 January 2010

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160802155294

zbMATH Keywords

numerical experimentslarge-scale problemPDE-constrained optimizationtrust-region methodsKarush-Kuhn-Tucker (KKT) systembox-constrained nonlinear equations

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Numerical methods based on nonlinear programming (49M37) Interior-point methods (90C51) Existence theories for optimal control problems involving partial differential equations (49J20)

Uses Software

• HSL
• STRSCNE

Cites Work

• On affine-scaling interior-point Newton methods for nonlinear minimization with bound constraints
• Optimization techniques for solving elliptic control problems with control and state constraints. I: Boundary control
• Solving elliptic control problems with interior point and SQP methods: Control and state constraints
• An interior-point method for solving box-constrained underdetermined nonlinear systems
• An affine scaling trust-region approach to bound-constrained nonlinear systems
• STRSCNE: a scaled trust-region solver for constrained nonlinear equations
• Preconditioning indefinite systems in interior point methods for optimization
• An affine scaling trust-region algorithm with interior backtracking technique for solving bound-constrained nonlinear systems
• Inexact constraint preconditioners for linear systems arising in interior point methods
• A Comparison of a Moreau--Yosida-Based Active Set Strategy and Interior Point Methods for Constrained Optimal Control Problems
• Numerical solution of saddle point problems
• Solution of Sparse Indefinite Systems of Linear Equations
• Numerical Optimization
• Augemented Lagrangian Techniques for Elliptic State Constrained Optimal Control Problems
• Krylov Subspace Methods for Saddle Point Problems with Indefinite Preconditioning
• A numerical evaluation of HSL packages for the direct solution of large sparse, symmetric linear systems of equations
• An interior global method for nonlinear systems with simple bounds
• Subspace Trust‐Region Methods for Large Bound‐Constrained Nonlinear Equations
• Optimization techniques for solving elliptic control problems with control and state constraints. II: Distributed control
• Benchmarking optimization software with performance profiles.

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