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27
Preconditioning techniques for large linear systems: A survey
 J. COMPUT. PHYS
, 2002
"... This article surveys preconditioning techniques for the iterative solution of large linear systems, with a focus on algebraic methods suitable for general sparse matrices. Covered topics include progress in incomplete factorization methods, sparse approximate inverses, reorderings, parallelization i ..."
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Cited by 105 (5 self)
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This article surveys preconditioning techniques for the iterative solution of large linear systems, with a focus on algebraic methods suitable for general sparse matrices. Covered topics include progress in incomplete factorization methods, sparse approximate inverses, reorderings, parallelization issues, and block and multilevel extensions. Some of the challenges ahead are also discussed. An extensive bibliography completes the paper.
Newton's Method For Large BoundConstrained Optimization Problems
 SIAM JOURNAL ON OPTIMIZATION
, 1998
"... We analyze a trust region version of Newton's method for boundconstrained problems. Our approach relies on the geometry of the feasible set, not on the particular representation in terms of constraints. The convergence theory holds for linearlyconstrained problems, and yields global and superlinea ..."
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Cited by 74 (4 self)
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We analyze a trust region version of Newton's method for boundconstrained problems. Our approach relies on the geometry of the feasible set, not on the particular representation in terms of constraints. The convergence theory holds for linearlyconstrained problems, and yields global and superlinear convergence without assuming neither strict complementarity nor linear independence of the active constraints. We also show that the convergence theory leads to an efficient implementation for large boundconstrained problems.
A scalable parallel algorithm for incomplete factor preconditioning
 SIAM Journal on Scientific Computing
"... Abstract. We describe a parallel algorithm for computing incomplete factor (ILU) preconditioners. The algorithm attains a high degree of parallelism through graph partitioning and a twolevel ordering strategy. Both the subdomains and the nodes within each subdomain are ordered to preserve concurren ..."
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Cited by 27 (2 self)
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Abstract. We describe a parallel algorithm for computing incomplete factor (ILU) preconditioners. The algorithm attains a high degree of parallelism through graph partitioning and a twolevel ordering strategy. Both the subdomains and the nodes within each subdomain are ordered to preserve concurrency. We show through an algorithmic analysis and through computational results that this algorithm is scalable. Experimental results include timings on three parallel platforms for problems with up to 20 million unknowns running on up to 216 processors. The resulting preconditioned Krylov solvers have the desirable property that the number of iterations required for convergence is insensitive to the number of processors.
A new active set algorithm for box constrained Optimization
 SIAM Journal on Optimization
, 2006
"... Abstract. An active set algorithm (ASA) for box constrained optimization is developed. The algorithm consists of a nonmonotone gradient projection step, an unconstrained optimization step, and a set of rules for branching between the two steps. Global convergence to a stationary point is established ..."
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Cited by 26 (6 self)
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Abstract. An active set algorithm (ASA) for box constrained optimization is developed. The algorithm consists of a nonmonotone gradient projection step, an unconstrained optimization step, and a set of rules for branching between the two steps. Global convergence to a stationary point is established. For a nondegenerate stationary point, the algorithm eventually reduces to unconstrained optimization without restarts. Similarly, for a degenerate stationary point, where the strong secondorder sufficient optimality condition holds, the algorithm eventually reduces to unconstrained optimization without restarts. A specific implementation of the ASA is given which exploits the recently developed cyclic Barzilai–Borwein (CBB) algorithm for the gradient projection step and the recently developed conjugate gradient algorithm CG DESCENT for unconstrained optimization. Numerical experiments are presented using box constrained problems in the CUTEr and MINPACK2 test problem libraries. Key words. nonmonotone gradient projection, box constrained optimization, active set algorithm,
On Centroidal Voronoi Tessellation  Energy Smoothness and Fast Computation
, 2008
"... Centroidal Voronoi tessellation (CVT) is a fundamental geometric structure that finds many applications in ..."
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Cited by 19 (9 self)
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Centroidal Voronoi tessellation (CVT) is a fundamental geometric structure that finds many applications in
An Algebraic Multilevel Multigraph Algorithm
 SIAM J. on Scientific Computing
"... . We describe an algebraic multilevel multigraph algorithm. Many of the multilevel components are generalizations of algorithms originally applied to general sparse Gaussian elimination. Indeed, general sparse Gaussian elimination with minimum degree ordering is a limiting case of our algorithm. Our ..."
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Cited by 12 (1 self)
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. We describe an algebraic multilevel multigraph algorithm. Many of the multilevel components are generalizations of algorithms originally applied to general sparse Gaussian elimination. Indeed, general sparse Gaussian elimination with minimum degree ordering is a limiting case of our algorithm. Our goal is to develop a procedure which has the robustness and simplicity of use of sparse direct methods, yet oers the opportunity to obtain the optimal or nearoptimal complexity typical of classical multigrid methods. Key words. algebraic multigrid, incomplete LU factorization, multigraph methods. AMS subject classications. 65M55, 65N55 1. Introduction. In this work, we develop a multilevelmultigraph algorithm. Algebraic multigrid methods are currently a topic of intense research interest [17, 18, 20, 46, 12, 48, 38, 11, 44, 3, 4, 1, 2, 5, 16, 7, 29, 28, 27, 42, 41, 21]. An excellent recent survey is given in Wagner [49]. In many \real world" calculations, direct methods are still wid...
GALAHAD, a library of threadsafe Fortran 90 Packages for LargeScale Nonlinear Optimization
, 2002
"... In this paper, we describe the design of version 1.0 of GALAHAD, a library of Fortran 90 packages for largescale largescale nonlinear optimization. The library particularly addresses quadratic programming problems, containing both interior point and active set variants, as well as tools for prepro ..."
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Cited by 12 (2 self)
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In this paper, we describe the design of version 1.0 of GALAHAD, a library of Fortran 90 packages for largescale largescale nonlinear optimization. The library particularly addresses quadratic programming problems, containing both interior point and active set variants, as well as tools for preprocessing such problems prior to solution. It also contains an updated version of the venerable nonlinear programming package, LANCELOT.
A LargeScale TrustRegion Approach to the Regularization of Discrete IllPosed Problems
 RICE UNIVERSITY
, 1998
"... We consider the problem of computing the solution of largescale discrete illposed problems when there is noise in the data. These problems arise in important areas such as seismic inversion, medical imaging and signal processing. We pose the problem as a quadratically constrained least squares pro ..."
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Cited by 12 (4 self)
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We consider the problem of computing the solution of largescale discrete illposed problems when there is noise in the data. These problems arise in important areas such as seismic inversion, medical imaging and signal processing. We pose the problem as a quadratically constrained least squares problem and develop a method for the solution of such problem. Our method does not require factorization of the coefficient matrix, it has very low storage requirements and handles the high degree of singularities arising in discrete illposed problems. We present numerical results on test problems and an application of the method to a practical problem with real data.
Preconditioning Newton's Method
 IN STUDIES IN NUMERICAL ANALYSIS (G.H. GOLUB, ED), THE MATHEMATICAL ASSOCIATION OF AMERICA
, 1998
"... The development of algorithms and software for the solution of largescale optimization problems ... ..."
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Cited by 11 (0 self)
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The development of algorithms and software for the solution of largescale optimization problems ...
Nonmonotone Trust Region Methods for Nonlinear Equality Constrained Optimization without a Penalty Function
 MATH. PROGRAM., SER. B
, 2000
"... We propose and analyze a class of penaltyfunctionfree nonmonotone trustregion methods for nonlinear equality constrained optimization problems. The algorithmic framework yields global convergence without using a merit function and allows nonmonotonicity independently for both, the constraint viol ..."
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Cited by 9 (5 self)
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We propose and analyze a class of penaltyfunctionfree nonmonotone trustregion methods for nonlinear equality constrained optimization problems. The algorithmic framework yields global convergence without using a merit function and allows nonmonotonicity independently for both, the constraint violation and the value of the Lagrangian function. Similar to the ByrdOmojokun class of algorithms, each step is composed of a quasinormal and a tangential step. Both steps are required to satisfy a decrease condition for their respective trustregion subproblems. The proposed mechanism for accepting steps combines nonmonotone decrease conditions on the constraint violation and/or the Lagrangian function, which leads to a flexibility and acceptance behavior comparable to filterbased methods. We establish the global convergence of the method. Furthermore, transition to quadratic local convergence is proved. Numerical tests are presented that confirm the robustness and efficiency of the approach.