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Algorithm 350: simplex method procedure employing Lu decomposition [H]

Authors:

Richard H. Bartels,

Gene H. GolubAuthors Info & Claims

Communications of the ACM, Volume 12, Issue 5

Pages 275 - 278

https://doi.org/10.1145/362946.362982

Published: 01 May 1969 Publication History

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Han DKaito KKobayashi KAoki K(2016)Management scheme of road pavements considering heterogeneous multiple life cycles changed by repeated maintenance workKSCE Journal of Civil Engineering10.1007/s12205-016-1461-x21:5(1747-1756)Online publication date: 30-Sep-2016
https://doi.org/10.1007/s12205-016-1461-x
Han D(2013)Stochastic Disaggregation and Aggregation of Localized Uncertainty in Pavement Deterioration ProcessJournal of The Korean Society of Civil Engineers10.12652/Ksce.2013.33.4.165133:4(1651-1664)Online publication date: 30-Jul-2013
https://doi.org/10.12652/Ksce.2013.33.4.1651
Pan P(2013)An affine-scaling pivot algorithm for linear programmingOptimization10.1080/02331934.2011.60657662:4(431-445)Online publication date: Apr-2013
https://doi.org/10.1080/02331934.2011.606576
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Algorithm 350: simplex method procedure employing Lu decomposition [H]
1. Mathematics of computing
  1. Mathematical analysis
    1. Mathematical optimization
      1. Continuous optimization
        Linear programming
2. Theory of computation
  1. Design and analysis of algorithms
    1. Mathematical optimization
      1. Continuous optimization
        Linear programming
  2. Randomness, geometry and discrete structures
    1. Error-correcting codes

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The simplex method of linear programming using LU decomposition

Standard computer implementations of Dantzig's simplex method for linear programming are based upon forming the inverse of the basic matrix and updating the inverse after every step of the method. These implementations have bad round-off error ...
Klee-Minty's LP and upper bounds for Dantzig's simplex method

Kitahara and Mizuno (2010) [2] get two upper bounds for the number of different basic feasible solutions generated by Dantzig's simplex method. The size of the bounds highly depends on the ratio between the maximum and the minimum values of all the ...
Implementing the simplex method as a cutting-plane method, with a view to regularization

We show that the simplex method can be interpreted as a cutting-plane method, assuming that a special pricing rule is used. This approach is motivated by the recent success of the cutting-plane method in the solution of special stochastic programming ...

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Published In

Communications of the ACM Volume 12, Issue 5

May 1969

95 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/362946

Editor:
M. Stuart Lynn
IBM Research Center, Houston, TX

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 May 1969

Published in CACM Volume 12, Issue 5

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Han DKaito KKobayashi KAoki K(2016)Management scheme of road pavements considering heterogeneous multiple life cycles changed by repeated maintenance workKSCE Journal of Civil Engineering10.1007/s12205-016-1461-x21:5(1747-1756)Online publication date: 30-Sep-2016
https://doi.org/10.1007/s12205-016-1461-x
Han D(2013)Stochastic Disaggregation and Aggregation of Localized Uncertainty in Pavement Deterioration ProcessJournal of The Korean Society of Civil Engineers10.12652/Ksce.2013.33.4.165133:4(1651-1664)Online publication date: 30-Jul-2013
https://doi.org/10.12652/Ksce.2013.33.4.1651
Pan P(2013)An affine-scaling pivot algorithm for linear programmingOptimization10.1080/02331934.2011.60657662:4(431-445)Online publication date: Apr-2013
https://doi.org/10.1080/02331934.2011.606576
Han DDo M(2012)Correction of Latent Errors in Pavement Deterioration Data using Statistical MethodsJournal of The Korean Society of Civil Engineers10.12652/Ksce.2012.32.6D.58732:6D(587-598)Online publication date: 15-Nov-2012
https://doi.org/10.12652/Ksce.2012.32.6D.587
Han DDo M(2012)Estimation of Life Expectancy and Budget Demands based on Maintenance StrategyJournal of The Korean Society of Civil Engineers10.12652/Ksce.2012.32.4D.34532:4D(345-356)Online publication date: 15-Jul-2012
https://doi.org/10.12652/Ksce.2012.32.4D.345
Fang HLeyffer SMunson T(2012)A pivoting algorithm for linear programming with linear complementarity constraintsOptimization Methods and Software10.1080/10556788.2010.51295627:1(89-114)Online publication date: Feb-2012
https://doi.org/10.1080/10556788.2010.512956
Daojian Liu Tianmin Huang (2010)An artificial variable RZ decision method for geometric superfluity of condition constraint in linear programming problem2010 IEEE International Conference on Intelligent Systems and Knowledge Engineering10.1109/ISKE.2010.5680794(56-59)Online publication date: Nov-2010
https://doi.org/10.1109/ISKE.2010.5680794
Hu JPan P(2008)An efficient approach to updating simplex multipliers in the simplex algorithmMathematical Programming: Series A and B10.5555/3113615.3114041114:2(235-248)Online publication date: 1-Aug-2008
https://dl.acm.org/doi/10.5555/3113615.3114041
Hu JPan P(2007)An efficient approach to updating simplex multipliers in the simplex algorithmMathematical Programming10.1007/s10107-007-0099-3114:2(235-248)Online publication date: 15-Feb-2007
https://doi.org/10.1007/s10107-007-0099-3
Pan PPan Y(2001)A phase-1 approach for the generalized simplex algorithmComputers & Mathematics with Applications10.1016/S0898-1221(01)00254-142:10-11(1455-1464)Online publication date: Nov-2001
https://doi.org/10.1016/S0898-1221(01)00254-1
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The simplex method of linear programming using LU decomposition

Klee-Minty's LP and upper bounds for Dantzig's simplex method

Implementing the simplex method as a cutting-plane method, with a view to regularization

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