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Linear programming
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== References == {{div col|colwidth=20em}} * {{cite journal |first=L. V. |last=Kantorovich |title=Об одном эффективном методе решения некоторых классов экстремальных проблем |trans-title=A new method of solving some classes of extremal problems |journal=[[Proceedings of the USSR Academy of Sciences|Doklady Akad Sci SSSR]] |volume=28 |year=1940 |pages=211–214 }} * F. L. Hitchcock: ''[https://onlinelibrary.wiley.com/doi/abs/10.1002/sapm1941201224 The distribution of a product from several sources to numerous localities]'', Journal of Mathematics and Physics, 20, 1941, 224–230. * G.B Dantzig: ''[https://books.google.com/books?id=ZpYca36h464C&dq=%22Maximization+of+a+linear+function+of+variables+subject+to+linear+inequalities%22&pg=PA24 Maximization of a linear function of variables subject to linear inequalities]'', 1947. Published pp. 339–347 in T.C. Koopmans (ed.):''Activity Analysis of Production and Allocation'', New York-London 1951 (Wiley & Chapman-Hall) * J. E. Beasley, editor. ''Advances in Linear and Integer Programming''. Oxford Science, 1996. (Collection of surveys) * {{cite journal|pages= 103–107|jstor=3689647|doi=10.1287/moor.2.2.103|title=New Finite Pivoting Rules for the Simplex Method|journal=Mathematics of Operations Research|volume=2|issue=2|year=1977|last1=Bland|first1=Robert G.}} * {{cite book |first=Karl-Heinz |last=Borgwardt |title=The Simplex Algorithm: A Probabilistic Analysis |series=Algorithms and Combinatorics |volume=1 |publisher=Springer-Verlag |date=1987}} (Average behavior on random problems) * Richard W. Cottle, ed. ''The Basic George B. Dantzig''. Stanford Business Books, Stanford University Press, Stanford, California, 2003. (Selected papers by [[George B. Dantzig]]) * George B. Dantzig and Mukund N. Thapa. 1997. ''Linear programming 1: Introduction''. Springer-Verlag. * {{cite book |first1=George B. |last1=Dantzig |first2=Mukund N. |last2=Thapa |date=2003 |title=Linear Programming 2: Theory and Extensions |publisher=Springer-Verlag}} (Comprehensive, covering e.g. [[simplex algorithm|pivoting]] and interior-point algorithms, large-scale problems, [[Dantzig–Wolfe decomposition|decomposition following Dantzig–Wolfe]] and [[Benders' decomposition|Benders]], and introducing [[stochastic programming]].) * {{cite book |doi=10.1016/S0167-5060(08)70734-9|pages=185–204|chapter=A Min-Max Relation for Submodular Functions on Graphs|title=Studies in Integer Programming|volume=1|series=Annals of Discrete Mathematics|year=1977|last1=Edmonds|first1=Jack|last2=Giles|first2=Rick|isbn=978-0-7204-0765-5}} * {{cite journal|first1=Komei|last1=Fukuda|first2=Tamás|last2=Terlaky|title=Criss-cross methods: A fresh view on pivot algorithms |journal=Mathematical Programming, Series B|volume=79|number=1–3|pages=369–395 |editor=Thomas M. Liebling |editor2=Dominique de Werra|year=1997|doi=10.1007/BF02614325|mr=1464775|citeseerx=10.1.1.36.9373|s2cid=2794181}} * {{cite book|last1=Gondzio|first1=Jacek|last2=Terlaky|first2=Tamás|chapter=3 A computational view of interior point methods|mr=1438311|title=Advances in linear and integer programming|pages=103–144|editor=J. E. Beasley|location=New York|publisher=Oxford University Press|year=1996|series=Oxford Lecture Series in Mathematics and its Applications|volume=4|chapter-url=http://www.maths.ed.ac.uk/~gondzio/CV/oxford.ps|id=[http://www.maths.ed.ac.uk/~gondzio/CV/oxford.ps Postscript file at website of Gondzio] and [http://www.cas.mcmaster.ca/~terlaky/files/dut-twi-94-73.ps.gz at McMaster University website of Terlaky]}} * {{cite book|last=Murty|first=Katta G.|author-link=Katta G. Murty|title=Linear programming|publisher=John Wiley & Sons, Inc.|location=New York|year=1983|pages=xix+482|isbn=978-0-471-09725-9|mr=720547|id=(comprehensive reference to classical approaches)}} * Evar D. Nering and [[Albert W. Tucker]], 1993, ''Linear Programs and Related Problems'', Academic Press. (elementary<!-- but profound -->) * {{cite book |first=M. |last=Padberg |title=Linear Optimization and Extensions, Second Edition |publisher=Springer-Verlag |date=1999}} (carefully written account of primal and dual simplex algorithms and projective algorithms, with an introduction to integer linear programming – featuring the [[traveling salesman problem]] for [[Odysseus]].) * {{cite book |author-link1=Christos H. Papadimitriou |first1=Christos H. |last1=Papadimitriou |first2=Kenneth |last2=Steiglitz |title=Combinatorial Optimization: Algorithms and Complexity |edition=Corrected republication with a new preface |publisher=Dover}} (computer science) * {{cite journal|first=Michael J. |last=Todd |date=February 2002 | title = The many facets of linear programming | journal = Mathematical Programming | volume = 91 | issue = 3 | doi = 10.1007/s101070100261 | pages=417–436|s2cid=6464735 }} (Invited survey, from the International Symposium on Mathematical Programming.) * {{cite book |first=Robert J. |last=Vanderbei |title=Linear Programming: Foundations and Extensions |year=2001 |publisher=Springer Verlag }} * {{cite book | last=Vazirani | first=Vijay V. | author-link=Vijay Vazirani | title=Approximation Algorithms | year=2001 | publisher=Springer-Verlag | isbn=978-3-540-65367-7 }} (Computer science) {{div col end}}
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