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Preconditioning indefinite systems in interior point methods for optimization
 COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
, 2004
"... Every Newton step in an interiorpoint method for optimization requires a solution of a symmetric indefinite system of linear equations. Most of today’s codes apply direct solution methods to perform this task. The use of logarithmic barriers in interior point methods causes unavoidable illcondit ..."
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Cited by 62 (16 self)
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Every Newton step in an interiorpoint method for optimization requires a solution of a symmetric indefinite system of linear equations. Most of today’s codes apply direct solution methods to perform this task. The use of logarithmic barriers in interior point methods causes unavoidable ill
Preconditioning Indefinite Systems in Interior Point Methods for Large Scale Linear Optimization
, 2007
"... 1 Preconditioning Indefinite Systems in Interior Point Methods for Large Scale Linear Optimization Abstract We discuss the use of preconditioned conjugate gradients method for solving the reducedKKT systems arising in interior point algorithms for linear programming. The (indefinite) augmented syste ..."
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Cited by 9 (3 self)
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1 Preconditioning Indefinite Systems in Interior Point Methods for Large Scale Linear Optimization Abstract We discuss the use of preconditioned conjugate gradients method for solving the reducedKKT systems arising in interior point algorithms for linear programming. The (indefinite) augmented
ATOMIC DECOMPOSITION BY BASIS PURSUIT
, 1995
"... The TimeFrequency and TimeScale communities have recently developed a large number of overcomplete waveform dictionaries  stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for d ..."
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Cited by 2694 (61 self)
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successfully only because of recent advances in linear programming by interiorpoint methods. We obtain reasonable success with a primaldual logarithmic barrier method and conjugategradient solver.
Constraint Preconditioning for Indefinite Linear Systems
 SIAM J. Matrix Anal. Appl
, 2000
"... . The problem of nding good preconditioners for the numerical solution of indenite linear systems is considered. Special emphasis is put on preconditioners that have a 2 2 block structure and which incorporate the (1; 2) and (2; 1) blocks of the original matrix. Results concerning the spectrum and ..."
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Cited by 108 (14 self)
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methods AMS subject classications. 65F10, 65F15, 65F50 1. Introduction. In this paper, we are concerned with investigating a new class of preconditioners for indenite systems of linear equations of a sort which arise in constrained optimization as well as in leastsquares, saddlepoint and Stokes
Weighted matchings for preconditioning symmetric indefinite linear systems
 SIAM J. Sci. Comput
, 2006
"... Abstract. Maximum weight matchings have become an important tool for solving highly indefinite unsymmetric linear systems, especially in direct solvers. In this study we investigate the benefit of reorderings and scalings based on symmetrized maximum weight matchings as a preprocessing step for inco ..."
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Cited by 24 (6 self)
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and comparisons with other solution methods for a diverse set of symmetric indefinite matrices, ranging from nonlinear elasticity to interior point optimization.
On polynomial preconditioning for indefinite hermitian matrices
, 1989
"... We are concerned with the minimal residual method combined with polynomial preconditioning for solving large linear systems Ax = b with indefinite Hermitian coefficient matrices A. The standard approach for choosing the polynomial preconditioner leads to preconditioned systems which are postive defi ..."
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Cited by 1 (0 self)
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We are concerned with the minimal residual method combined with polynomial preconditioning for solving large linear systems Ax = b with indefinite Hermitian coefficient matrices A. The standard approach for choosing the polynomial preconditioner leads to preconditioned systems which are postive
Symmetric indefinite systems for interior point methods
, 1993
"... We present a unified framework for solving linear and convex quadratic programs via interior point methods. At each iteration, this method solves an indefinite system whose matrix is [_~2 A v] instead of reducing to obtain the usual AD2A v system. This methodology affords two advantages: (1) it avo ..."
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Cited by 44 (2 self)
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We present a unified framework for solving linear and convex quadratic programs via interior point methods. At each iteration, this method solves an indefinite system whose matrix is [_~2 A v] instead of reducing to obtain the usual AD2A v system. This methodology affords two advantages: (1
ABSOLUTE VALUE PRECONDITIONING FOR SYMMETRIC INDEFINITE LINEAR SYSTEMS
, 2013
"... We introduce a novel strategy for constructing symmetric positive definite (SPD) preconditioners for linear systems with symmetric indefinite matrices. The strategy, called absolute value preconditioning, is motivated by the observation that the preconditioned minimal residual method with the invers ..."
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Cited by 3 (3 self)
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We introduce a novel strategy for constructing symmetric positive definite (SPD) preconditioners for linear systems with symmetric indefinite matrices. The strategy, called absolute value preconditioning, is motivated by the observation that the preconditioned minimal residual method
Interior Point Methods For Global Optimization
 INTERIOR POINT METHODS OF MATHEMATICAL PROGRAMMING
, 1996
"... Interior point methods, originally invented in the context of linear programming, have found a much broader range of applications, including global optimization problems that arise in engineering, computer science, operations research, and other disciplines. This chapter overviews the conceptual bas ..."
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Cited by 4 (1 self)
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Interior point methods, originally invented in the context of linear programming, have found a much broader range of applications, including global optimization problems that arise in engineering, computer science, operations research, and other disciplines. This chapter overviews the conceptual
Convergence acceleration of preconditioned indefinite systems
, 1997
"... for second order elliptic boundary value problems ..."
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