ABS methods for continuous and integer linear equations and optimization

DOI10.1007/s10100-009-0128-9zbMath1204.65064OpenAlexW2018343880MaRDI QIDQ623802

Elena Bodon, Emilio Spedicato, Zun-Quan Xia, Nezam Mahdavi-Amiri

Publication date: 8 February 2011

Published in: CEJOR. Central European Journal of Operations Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10100-009-0128-9

zbMATH Keywords

linear systemssimplex methodprimal-dual interior point methodsquasi-Newton equationABS methodsABSPACKDiophantine linear systemsEgerváry rank reduction matrix updatefeasible direction methods for linearly constrained optimization

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Numerical computation of solutions to systems of equations (65H10) Linear programming (90C05) Iterative numerical methods for linear systems (65F10)

Related Items (10)

Real and Integer Extended Rank Reduction Formulas and Matrix Decompositions: A Review ⋮ Fuzzy LR linear systems: quadratic and least squares models to characterize exact solutions and an algorithm to compute approximate solutions ⋮ Special issue in honour of Jenő Egerváry ⋮ An efficient algorithm for sparse null space basis problem using ABS methods ⋮ Extended rank reduction formulas containing Wedderburn and Abaffy-Broyden-Spedicato rank reducing processes ⋮ A generalization of the ABS algorithms and its application to some special real and integer matrix factorizations ⋮ On generalized Schur complement of matrices and its applications to real and integer matrix factorizations ⋮ General solution of full row rank linear systems of equations using a new compression ABS model ⋮ Rank reduction processes for solving linear Diophantine systems and integer factorizations: a review ⋮ Extended integer rank reduction formulas and Smith normal form

Cites Work

• A class of scaled direct methods for linear systems
• On the numerical stability of Huang's and related methods
• A class of direct methods for linear systems
• On solving linear Diophantine systems using generalized Rosser's algorithm
• Integer extended ABS algorithms and possible control of intermediate results for linear Diophantine systems
• A direct method for the general solution of a system of linear equations
• Solution of linear least squares via the ABS algorithm
• Computational experiments with ABS algorithms for KKT linear systems
• The implicit LX method of the ABS class
• A class of ABS algorithms for Diophantine linear systems
• Symmetric and non-symmetric ABS methods for solving Diophantine systems of equations
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