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A QMR-based interior-point algorithm for solving linear programs

https://doi.org/10.1007/bf02614383
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/978-1-4613-9353-5_6openalex-snapshot
Transpose-Free Quasi-Minimal Residual Methods for Non-Hermitian Linear Systems
inferredcites →https://doi.org/10.1007/978-1-4613-9617-8_2openalex-snapshot
A Primal-Dual Interior Point Algorithm for Linear Programming
inferredcites →https://doi.org/10.1007/978-1-4613-9617-8_8openalex-snapshot
Pathways to the Optimal Set in Linear Programming
inferredcites →https://doi.org/10.1007/978-3-0348-8619-2_5openalex-snapshot
Quasi-Kernel Polynomials and Convergence Results for Quasi-Minimal Residual Iterations
inferredcites →https://doi.org/10.1007/bf01385726openalex-snapshot
QMR: a quasi-minimal residual method for non-Hermitian linear systems
inferredcites →https://doi.org/10.1007/bf01581257openalex-snapshot
Symmetric indefinite systems for interior point methods
inferredcites →https://doi.org/10.1007/bf01582151openalex-snapshot
A primal—dual infeasible-interior-point algorithm for linear programming
inferredcites →https://doi.org/10.1007/bf01582905openalex-snapshot
Computational results of an interior point algorithm for large scale linear programming
inferredcites →https://doi.org/10.1007/bf01585158openalex-snapshot
Solving symmetric indefinite systems in an interior-point method for linear programming
inferredcites →https://doi.org/10.1007/bf01587075openalex-snapshot
Interior path following primal-dual algorithms. part I: Linear programming
inferredcites →https://doi.org/10.1007/bf01587095openalex-snapshot
An implementation of Karmarkar's algorithm for linear programming
inferredcites →https://doi.org/10.1007/bf01934996openalex-snapshot
A survey of preconditioned iterative methods for linear systems of algebraic equations
inferredcites →https://doi.org/10.1007/bf02206815openalex-snapshot
A simplified homogeneous and self-dual linear programming algorithm and its implementation
inferredcites →https://doi.org/10.1007/bf02579150openalex-snapshot
A new polynomial-time algorithm for linear programming
inferredcites →https://doi.org/10.1007/bfb0042787openalex-snapshot
Centered newton method for mathematical programming
inferredcites →https://doi.org/10.1016/0024-3795(91)90275-2openalex-snapshot
Computational experience with a primal-dual interior point method for linear programming
inferredcites →https://doi.org/10.1016/0377-2217(90)90098-vopenalex-snapshot
Progress in mathematical programming — interior-point and related methods
inferredcites →https://doi.org/10.1017/s0962492900002245openalex-snapshot
Iterative solution of linear systems
inferredcites →https://doi.org/10.1137/0613022openalex-snapshot
Preconditioners for Indefinite Systems Arising in Optimization
inferredcites →https://doi.org/10.1137/0708060openalex-snapshot
Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations
inferredcites →https://doi.org/10.1137/0712047openalex-snapshot
Solution of Sparse Indefinite Systems of Linear Equations
inferredcites →https://doi.org/10.1137/0802022openalex-snapshot
On Implementing Mehrotra’s Predictor–Corrector Interior-Point Method for Linear Programming
inferredcites →https://doi.org/10.1137/0902001openalex-snapshot
Efficient Implementation of a Class of Preconditioned Conjugate Gradient Methods
inferredcites →https://doi.org/10.1137/0914009openalex-snapshot
An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices
inferredcites →https://doi.org/10.1137/0915022openalex-snapshot
An Implementation of the QMR Method Based on Coupled Two-Term Recurrences
inferredcites →https://doi.org/10.1287/moor.24.1.50openalex-snapshot
Convergence of a Class of Inexact Interior-Point Algorithms for Linear Programs
inferredcites →https://doi.org/10.6028/jres.049.044openalex-snapshot
Methods of conjugate gradients for solving linear systems

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1002/nme.1461openalex-snapshot
A modified SSOR preconditioner for sparse symmetric indefinite linear systems of equations
inferred← citeshttps://doi.org/10.1007/0-306-48026-3_1openalex-snapshot
On the Numerical Solution of Finite-Dimensional Variational Inequalities by an Interior Point Method
inferred← citeshttps://doi.org/10.1007/978-3-0348-8849-3_2openalex-snapshot
Preconditioners for Karush-Kuhn-Tucker Matrices Arising in the Optimal Control of Distributed Systems
inferred← citeshttps://doi.org/10.1007/978-3-319-07236-4_5openalex-snapshot
Low-Rank Cholesky Factor Krylov Subspace Methods for Generalized Projected Lyapunov Equations
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A Study of the Complexity of an Infeasible Predictor-Corrector Variant of Mehrotra Algorithm
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On the Complexity of a Mehrotra-Type Predictor-Corrector Algorithm
inferred← citeshttps://doi.org/10.1007/s006070050012openalex-snapshot
Eigenvalue Relations and Conditions of Matrices Arising in Linear Programming
inferred← citeshttps://doi.org/10.1007/s10589-006-9006-8openalex-snapshot
Preconditioning and iterative solution of symmetric indefinite linear systems arising from interior point methods for linear programming
inferred← citeshttps://doi.org/10.1007/s10589-007-9035-yopenalex-snapshot
On the iterative solution of KKT systems in potential reduction software for large-scale quadratic problems
inferred← citeshttps://doi.org/10.1007/s10589-007-9157-2openalex-snapshot
A stable primal–dual approach for linear programming under nondegeneracy assumptions
inferred← citeshttps://doi.org/10.1007/s10589-008-9226-1openalex-snapshot
On mutual impact of numerical linear algebra and large-scale optimization with focus on interior point methods
inferred← citeshttps://doi.org/10.1007/s10589-010-9361-3openalex-snapshot
Matrix-free interior point method
inferred← citeshttps://doi.org/10.1007/s10589-019-00103-yopenalex-snapshot
Implementation of interior-point methods for LP based on Krylov subspace iterative solvers with inner-iteration preconditioning
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A global optimization method for semi-supervised clustering
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On the convergence of a predictor-corrector variant algorithm
inferred← citeshttps://doi.org/10.1016/0168-9274(95)00089-5openalex-snapshot
Software for simplified Lanczos and QMR algorithms
inferred← citeshttps://doi.org/10.1016/j.apnum.2020.11.008openalex-snapshot
A modified SSOR-like preconditioner for non-Hermitian positive definite matrices
inferred← citeshttps://doi.org/10.1016/j.ifacol.2018.11.064openalex-snapshot
Preconditioned Krylov iterations and condensing in interior point MPC method
inferred← citeshttps://doi.org/10.1016/s0168-9274(98)00024-5openalex-snapshot
On the implementation of the Dirichlet-to-Neumann radiation condition for iterative solution of the Helmholtz equation
inferred← citeshttps://doi.org/10.1016/s0377-0427(00)00408-8openalex-snapshot
Symbiosis between linear algebra and optimization
inferred← citeshttps://doi.org/10.1016/s0898-1221(02)00153-0openalex-snapshot
The convergence of an interior-point method using modified search directions in final iterations
inferred← citeshttps://doi.org/10.1017/s0334270000011267openalex-snapshot
Final iterations in interior point methods – preconditioned conjugate gradients and modified search directions
inferred← citeshttps://doi.org/10.1017/s0962492904000212openalex-snapshot
Numerical solution of saddle point problems
inferred← citeshttps://doi.org/10.1023/a:1016614603137openalex-snapshot
Adaptive use of iterative methods in predictor–corrector interior point methods for linear programming
inferred← citeshttps://doi.org/10.1023/a:1018369223322openalex-snapshot
A Computational Study of the Homogeneous Algorithm for Large-scale Convex Optimization
inferred← citeshttps://doi.org/10.1023/a:1022663100715openalex-snapshot
Inexact Interior-Point Method
inferred← citeshttps://doi.org/10.1080/10556789908805752openalex-snapshot
An inexact interior point method for monotone NCP
inferred← citeshttps://doi.org/10.1088/0266-5611/17/6/319openalex-snapshot
Preconditioned all-at-once methods for large, sparse parameter estimation problems
inferred← citeshttps://doi.org/10.1090/mcom/4074openalex-snapshot
QQMR: A structure preserving quaternion quasi-minimal residual method
inferred← citeshttps://doi.org/10.1109/tac.2013.2253218openalex-snapshot
A Distributed Newton Method for Network Utility Maximization–I: Algorithm
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Solving scalarized multi‐objective network flow problems using an interior point method
inferred← citeshttps://doi.org/10.1137/040615614openalex-snapshot
Weighted Matchings for Preconditioning Symmetric Indefinite Linear Systems
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On Large-Scale Diagonalization Techniques for the Anderson Model of Localization
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On Large-Scale Diagonalization Techniques for the Anderson Model of Localization
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Inertia-Revealing Preconditioning For Large-Scale Nonconvex Constrained Optimization
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Algebraic Multilevel Preconditioner for the Helmholtz Equation in Heterogeneous Media
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An Interior-Point Algorithm for Large-Scale Nonlinear Optimization with Inexact Step Computations
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A Stable and Efficient Method for Solving a Convex Quadratic Program with Application to Optimal Control
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A Symmetric Reduction of the NT Direction
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On Barrier and Modified Barrier Multigrid Methods for Three-Dimensional Topology Optimization
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Convergence Conditions and Krylov Subspace--Based Corrections for Primal-Dual Interior-Point Method
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Optimal Truss Design by Interior-Point Methods
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Convergence Analysis of Inexact Infeasible-Interior-Point Algorithms for Solving Linear Programming Problems
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Inversion of 3D electromagnetic data in frequency and time domain using an inexact all-at-once approach
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Convergence of a Class of Inexact Interior-Point Algorithms for Linear Programs
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Kernel Fisher Discriminants
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Irregularity mitigation and portability abstractions for accelerated sparse matrix factorization
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Using incomplete indefinite $LDL^T$ preconditioning for inexact interior point methods for linear programming
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On barrier and modified barrier multigrid methods for 3d topology optimization
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High Performance Block Incomplete LU Factorization
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On the application of iterative solvers to KKT systems in Interior Point methods for Large-Scale Quadratic Programming problems
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