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References (30)
-
I. Argyros (1990)
A mesh-independence principle for nonlinear operator equations and their discretizations under mild differentiability conditionsComputing, 45
-
O. Axelsson (1993)
On mesh independence and Newton-type methodsApplications of Mathematics, 38
-
P. Gill, W. Murray, M. Saunders (2002)
SNOPT: An SQP Algorithm for Large-Scale Constrained OptimizationSIAM Rev., 47
-
P. Farrell, D. Ham, S. Funke, M. Rognes (2012)
Automated Derivation of the Adjoint of High-Level Transient Finite Element ProgramsArXiv, abs/1204.5577
-
A. Dontchev, W. Hager, V. Veliov (2000)
Uniform Convergence and Mesh Independence of Newton's Method for Discretized Variational ProblemsSIAM J. Control. Optim., 39
-
A. Henrot (2003)
Minimization problems for eigenvalues of the LaplacianJournal of Evolution Equations, 3
-
R. Byrd, P. Lu, J. Nocedal, C. Zhu (1995)
A Limited Memory Algorithm for Bound Constrained OptimizationSIAM J. Sci. Comput., 16
-
C. Kelley, E. Sachs (1986)
Quasi Newton methods and unconstrained optimal control problems1986 25th IEEE Conference on Decision and Control
-
F. Potra, W. Rheinboldt, K. Böhmer, E. Allgower (1986)
A mesh-independence principle for operator equations and their discretizationsSIAM Journal on Numerical Analysis, 23
-
Xiaodong Huang, Y. Xie (2007)
Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization methodFinite Elements in Analysis and Design, 43
-
A. Wächter, L. Biegler (2006)
On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programmingMathematical Programming, 106
-
C. Kelley, E. Sachs (1990)
Approximate quasi-Newton methodsMathematical Programming, 48
-
A. Logg, K. Mardal, G. Wells (2012)
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book -
M. Hintermüller, M. Ulbrich (2004)
A mesh-independence result for semismooth Newton methodsMathematical Programming, 101
-
E. Allgower, K. Böhmer, S. Cormick (1981)
Discrete correction methods for operator equations -
P. Deuflhard, F. Potra (1992)
Asymptotic mesh independence of Newton-Galerkin methods via a refined Mysovskii theoremSIAM Journal on Numerical Analysis, 29
-
K Mardal, R. Winther (2011)
Preconditioning discretizations of systems of partial differential equationsNumerical Linear Algebra with Applications, 18
-
W. Alt (2001)
Mesh-Independence of the Lagrange–Newton Method for Nonlinear Optimal Control Problems and their DiscretizationsAnnals of Operations Research, 101
-
E. Allgower, S. McCormick, D. Pryor (1979)
A general mesh independence principle for Newton's method applied to second order boundary value problemsComputing, 23
-
R. Herzog, K. Kunisch (2010)
Algorithms for PDE‐constrained optimizationGAMM‐Mitteilungen, 33
-
S. Volkwein (2000)
Mesh-Independence for an Augmented Lagrangian-SQP Method in Hilbert SpacesSIAM J. Control. Optim., 38
-
I. Fried (1972)
Bounds on the extremal eigenvalues of the finite element stiffness and mass matrices and their spectral condition numberJournal of Sound and Vibration, 22
-
M. Ulbrich (2002)
Semismooth Newton Methods for Operator Equations in Function SpacesSIAM J. Optim., 13
-
R. Kirby (2010)
From Functional Analysis to Iterative MethodsSIAM Rev., 52
-
E. Allgower, S. McCormick (1978)
Newton's method with mesh refinements for numerical solution of nonlinear two-point boundary value problemsNumerische Mathematik, 29
-
C. Kelley, E. Sachs (1992)
Mesh independence of the gradient projection method for optimal control problemsSiam Journal on Control and Optimization, 30
-
M. Heinkenschloss (1993)
Mesh Independence for Nonlinear Least Squares Problems with Norm ConstraintsSIAM J. Optim., 3
-
S. Ta'asan, G. Kuruvila, M. Salas (1992)
Aerodynamic design and optimization in one shot -
M. Heinkenschloss, Manfred Laumen, E. Sachs (1991)
Gauss-Newton methods with grid refinement -
S. McCormick (1978)
A revised mesh refinement strategy for newton’s method applied to nonlinear two-point boundary value problems
- Publisher
- Springer International Publishing
- Copyright
- © The Author(s) 2017
- ISBN
- 978-3-319-59482-8
- Pages
- 53 –78
- DOI
- 10.1007/978-3-319-59483-5_2
- Publisher site
- See Chapter on Publisher Site
Abstract
[Computationally solving an optimisation problem on Hilbert spaces requires discretisation and the application of an optimisation method to the resulting finite-dimensional problem. In this context, mesh-independent convergence of the optimisation algorithm means that, for a discretisation given on a sufficiently fine mesh, the number of iterations required to solve the optimisation problem to a given tolerance is bounded.]
Published: Jul 8, 2017