Domain Decomposition Methods for Linear-Quadratic Elliptic Optimal Control Problems

Domain Decomposition Methods for Linear-Quadratic Elliptic Optimal Control Problems

[1]  George Biros,et al.  Parallel Lagrange-Newton-Krylov-Schur Methods for PDE-Constrained Optimization. Part I: The Krylov-Schur Solver , 2005, SIAM J. Sci. Comput..

[2]  R. Freund,et al.  Software for simplified Lanczos and QMR algorithms , 1995 .

[3]  James Demmel,et al.  Applied Numerical Linear Algebra , 1997 .

[4]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[5]  S. Ravindran,et al.  Analysis and approximation of optimal control problems for a simplified Ginzburg-Landau model of superconductivity , 1997 .

[6]  L. Trefethen,et al.  Numerical linear algebra , 1997 .

[7]  R. Freund,et al.  QMR: a quasi-minimal residual method for non-Hermitian linear systems , 1991 .

[8]  J. Lions,et al.  Sur le contrôle parallèle des systèmes distribués , 1998 .

[9]  O. Widlund,et al.  Balancing Neumann‐Neumann methods for incompressible Stokes equations , 2001 .

[10]  Volker Schulz,et al.  Interior point multigrid methods for topology optimization , 2000 .

[11]  O. Widlund.  Domain Decomposition Algorithms , 1993 .

[12]  Jorge Nocedal,et al.  Automatic Preconditioning by Limited Memory Quasi-Newton Updating , 1999, SIAM J. Optim..

[13]  Barry Smith,et al.  Domain Decomposition Methods for Partial Differential Equations , 1997 .

[14]  Gene H. Golub,et al.  A Note on Preconditioning for Indefinite Linear Systems , 1999, SIAM J. Sci. Comput..

[15]  A. Wathen,et al.  Fast iterative solution of stabilised Stokes systems part II: using general block preconditioners , 1994 .

[16]  A. Bounaim,et al.  A Lagrangian Approach to a DDM for an Optimal Control Problem , 1998 .

[17]  Nicholas I. M. Gould,et al.  Constraint Preconditioning for Indefinite Linear Systems , 2000, SIAM J. Matrix Anal. Appl..

[18]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[19]  Zi-Cai Li,et al.  Schwarz Alternating Method , 1998 .

[20]  A. Hadjidimos.  Iterative methods for the solution of linear systems , 1989 .

[21]  Nicholas I. M. Gould,et al.  On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization , 2001, SIAM J. Sci. Comput..

[22]  Olof B. Widlund,et al.  Domain Decomposition Algorithms for Indefinite Elliptic Problems , 2017, SIAM J. Sci. Comput..

[23]  R. Freund,et al.  A new Krylov-subspace method for symmetric indefinite linear systems , 1994 .

[24]  Michael A. Saunders,et al.  Preconditioners for Indefinite Systems Arising in Optimization , 1992, SIAM J. Matrix Anal. Appl..

[25]  W. Symes,et al.  Conjugate residual methods for almost symmetric linear systems , 1992 .

[26]  Barry F. Smith,et al.  Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations , 1996 .

[27]  Jinchao Xu,et al.  A preconditioned GMRES method for nonsymmetric or indefinite problems , 1992 .

[28]  M. Saunders,et al.  Solution of Sparse Indefinite Systems of Linear Equations , 1975 .

[29]  P. Oswald,et al.  Remarks on the Abstract Theory of Additive and Multiplicative Schwarz Algorithms , 1995 .

[30]  Ekkehard W. Sachs,et al.  Block Preconditioners for KKT Systems in PDE—Governed Optimal Control Problems , 2001 .

[31]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[32]  P. Bassanini,et al.  Elliptic Partial Differential Equations of Second Order , 1997 .

[33]  James E. Dennis,et al.  A Comparison of Nonlinear Programming Approaches to an Elliptic Inverse Problem and a New Domain Dec , 1994 .

[34]  Olof B. Widlund,et al.  Domain Decomposition Algorithms with Small Overlap , 1992, SIAM J. Sci. Comput..

[35]  J. Mandel.  Balancing domain decomposition , 1993 .

[36]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[37]  Jinchao Xu,et al.  Some Estimates for a Weighted L 2 Projection , 1991 .

[38]  Ladislav Lukand Jan Vl.  Indefinitely Preconditioned Inexact Newton Method for Large Sparse Equality Constrained Non-linear Programming Problems , 1998 .

[39]  Jinchao Xu,et al.  Iterative Methods by Space Decomposition and Subspace Correction , 1992, SIAM Rev..

[40]  Gene H. Golub,et al.  Matrix computations , 1983 .

[41]  Tony F. Chan,et al.  On the Relationship between Overlapping and Nonoverlapping Domain Decomposition Methods , 1992, SIAM J. Matrix Anal. Appl..

[42]  Jan Vlcek,et al.  Indefinitely preconditioned inexact Newton method for large sparse equality constrained non-linear programming problems , 1998, Numer. Linear Algebra Appl..

[43]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[44]  Jinchao Xu.  A new class of iterative methods for nonselfadjoint or indefinite problems , 1992 .

[45]  Matthias Heinkenschloss,et al.  Balancing Neumann-Neumann Methods for Elliptic Optimal Control Problems , 2005 .

[46]  Matthias Heinkenschloss,et al.  Preconditioners for Karush-Kuhn-Tucker Matrices Arising in the Optimal Control of Distributed Systems , 1998 .

[47]  Jean E. Roberts,et al.  Mixed and hybrid finite element methods , 1987 .

[48]  Jean-David Benamou,et al.  A Domain Decomposition Method with Coupled Transmission Conditions for the Optimal Control of Systems Governed by Elliptic Partial Differential Equations , 1996 .

[49]  T. Chan,et al.  Domain decomposition algorithms , 1994, Acta Numerica.

[50]  Jack Dongarra,et al.  Numerical Linear Algebra for High-Performance Computers , 1998 .

[51]  Gene H. Golub,et al.  On Solving Block-Structured Indefinite Linear Systems , 2003, SIAM J. Sci. Comput..

[52]  Barry F. Smith,et al.  Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions , 1994 .

[53]  Eberhard Zeidler,et al.  Applied Functional Analysis: Main Principles and Their Applications , 1995 .

[54]  William G. Litvinov,et al.  Optimization in Elliptic Problems with Applications to Mechanics of Deformable Bodies and Fluid Mechanics , 2000 .

[55]  Xiao,et al.  MULTIPLICATIVE SCHWARZ ALGORITHMS FOR SOME NONSYMMETRIC AND INDEFINITE PROBLEMS , 1993 .

[56]  Max Gunzburger,et al.  Finite element approximations of an optimal control problem associated with the scalar Ginzburg-Landau equation , 1991 .

[57]  O. Widlund,et al.  Schwarz Methods of Neumann-Neumann Type for Three-Dimensional Elliptic Finite Element Problems , 1993 .

[58]  Olof B. Widlund,et al.  To overlap or not to overlap: a note on a domain decomposition method for elliptic problems , 1989 .

[59]  E. Haber,et al.  Preconditioned all-at-once methods for large, sparse parameter estimation problems , 2001 .

[60]  Hoang Nguyen,et al.  Neumann-Neumann Domain Decomposition Preconditioners for Linear-Quadratic Elliptic Optimal Control Problems , 2006, SIAM J. Sci. Comput..

[61]  Andrew J. Wathen,et al.  Schur complement preconditioning for elliptic systems of partial differential equations , 2003, Numer. Linear Algebra Appl..

[62]  S. Eisenstat,et al.  Variational Iterative Methods for Nonsymmetric Systems of Linear Equations , 1983 .

[63]  Eberhard Zeidler,et al.  Applied Functional Analysis , 1995 .

[64]  Eugene M. Cliff,et al.  Thermal-fluid control via finite-dimensional approximation , 1996 .

[65]  O. Ghattas,et al.  Parallel Preconditioners for KKT Systems Arising in Optimal Control of Viscous Incompressible Flows , 2000 .

[66]  V. A. Barker,et al.  Finite element solution of boundary value problems , 1984 .

[67]  A. H. Schatz,et al.  An observation concerning Ritz-Galerkin methods with indefinite bilinear forms , 1974 .

[68]  J. Lions.  Optimal Control of Systems Governed by Partial Differential Equations , 1971 .

[69]  R. Hoppe,et al.  Primal-Dual Newton-Type Interior-Point Method for Topology Optimization , 2002 .

[70]  E. Haber,et al.  A multigrid method for distributed parameter estimation problems. , 2003 .