Documenta Mathematica Optimization Stories - Mathematics

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22 Eberhard Knobloch Figure 2: First page of Leibniz’s treatise Arithmetical quadrature of the circle etc. (By courtesy of the Gottfried Wilhelm Leibniz Library, Hannover. Shelf mark LH XXXV 2,1 folio 7r) Documenta Mathematica · Extra Volume ISMP (2012) 19–23
Leibniz and the Infinite 23 Because instead of the infinite and the infinitely small one takes quantities that are as large or as small as it is necessary so that the error is smaller than the given error so that one differs from the style of Archimedes only by the expressions which are more direct in our method and more suitable for the art of invention. The story convincingly demonstrates the correctness of his saying: “Those who know me only by my publications don’t know me.” References [1] E. Knobloch, Leibniz’s rigorous foundation of infinitesimal geometry by means of Riemannian sums, Synthese 133 (2002), 59–73. [2] [2] E. Knobloch, Galileo and German thinkers: Leibniz, in: L. Pepe (ed.), Galileo e la scuola galileiana nelle Università del Seicento, Cooperativa Libraria Universitaria Bologna, Bologna 2011, pp. 127–139. Eberhard Knobloch Berlin-Brandenburg Academy of Sciences and Humanities Technische Universität Berlin H 72 Straße des 17. Juni 135 10623 Berlin eberhard.knobloch@tu-berlin.de Documenta Mathematica · Extra Volume ISMP (2012) 19–23
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Page 5 and 6: Richard W. Cottle William Karush an
Page 7 and 8: Documenta Math. 1 Preface When in d
Page 9 and 10: Documenta Math. 3 Introduction When
Page 11 and 12: Introduction 5 Finally, I would lik
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Page 15 and 16: Documenta Math. 9 Jiu Zhang Suan Sh
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Page 27: Leibniz and the Infinite 21 finally
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Column Generation for Linear and In
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Documenta Math. 75 Who Solved the H
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2 A first counterexample Who Solved
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Who Solved the Hirsch Conjecture? 7
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Documenta Math. 87 Pope Gregory, th
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Pope Gregory, the Calendar, and Con
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Documenta Math. 95 Löwner-John Ell
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2 The ellipsoids Löwner-John Ellip
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Löwner-John Ellipsoids 99 For maxi
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H + Löwner-John Ellipsoids 101 t P
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Löwner-John Ellipsoids 103 any odd
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Löwner-John Ellipsoids 105 [23] P.
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Documenta Math. 107 A Brief History
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A Brief History 109 first-generatio
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A Brief History 111 developments ar
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A Brief History 113 in practice. Ka
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A Brief History 115 that LPs with s
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Version-to-Version Speedup 10 9 8 7
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A Brief History 119 [10] Crowder, H
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A Brief History 121 Robert E. Bixby
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Documenta Math. 123 Discrete Optimi
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Discrete Optimization Stories 125 I
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Documenta Math. 127 The Origins of
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Minimal Spanning Tree Algorithm 129
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Documenta Math. 143 The Coming of t
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The Sixties The Coming of the Matro
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The Coming of the Matroids 147 Figu
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The Coming of the Matroids 149 desc
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The Coming of the Matroids 151 In f
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The Coming of the Matroids 153 [10]
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Documenta Math. 155 On the History
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On the History of the Shortest Path
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Documenta Math. 169 On the History
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Transportation and Maximum Flow Pro
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Documenta Math. 181 Edmonds, Matchi
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The Birth of Polyhedral Combinatori
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Documenta Math. 199 Flinders Petrie
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The travelling salesman problem Fli
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Flinders Petrie 203 accuracy. The r
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Flinders Petrie 205 Figure 3: Paper
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Flinders Petrie 207 Figure 4: Petri
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Flinders Petrie 209 [8] F. R. Hodso
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Documenta Math. 211 D. Ray Fulkerso
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D. Ray Fulkerson and Project Schedu
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G 1 2 D. Ray Fulkerson and Project
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Documenta Math. 221 The Ongoing Sto
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The Ongoing Story of Gomory Cuts 22
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Acknowledgement The Ongoing Story o
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Documenta Math. 227 Markowitz and M
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Markowitz and Manne + Eastman + Lan
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Documenta Math. 239 Ronald Graham:
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Ronald Graham: Foundations of Onlin
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Machines Ronald Graham: Foundations
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Ronald Graham: Foundations of Onlin
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Documenta Math. 247 Continuous Opti
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Figure 1: Minkowski’s grave ( c
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Documenta Math. 251 Cauchy and the
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Cauchy and the Gradient Method 253
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Documenta Math. 255 William Karush
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William Karush and the KKT Theorem
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Documenta Math. 271 Nelder, Mead, a
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Nelder, Mead, and the Other Simplex
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Nelder, Mead, and the Other Simplex
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Documenta Math. 277 Subgradient Opt
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Subgradient Optimization in Nonsmoo
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Documenta Math. 291 A Science Ficti
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A Science Fiction Story in Nonsmoot
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Documenta Math. 301 Broyden Updatin
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Broyden Updating, the Good and the
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Documenta Math. 317 Carathéodory o
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Carathéodory on the Road to the Ma
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Documenta Math. 331 The Cold War an
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The Cold War and the Maximum Princi
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Documenta Math. 345 The Princess an
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yB y The Princess and Infinite-Dime
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x2 The Princess and Infinite-Dimens
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The Princess and Infinite-Dimension
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Documenta Math. 357 Computing Stori
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Documenta Math. 359 A Brief History
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A Brief History of NP-Completeness
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Documenta Math. 377 On the Evolutio
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Optimization Modeling Systems 379 T
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Optimization Modeling Systems 381 m
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Optimization Modeling Systems 383 C
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Optimization Modeling Systems 385 a
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Optimization Modeling Systems 387 e
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Documenta Math. 389 Who Invented th
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Who Invented the Reverse Mode of Di
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Documenta Math. 401 Gordon Moore an
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Gordon Moore and His Law 403 Figure
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Gordon Moore and His Law 405 jector
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!$ ? !$ > !$ & Gordon Moore and His
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� � � � � � � � �
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Gordon Moore and His Law 415 [14] M
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Documenta Math. 417 More Optimizati
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Documenta Math. 419 Voronoi Diagram
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Voronoi Diagrams and Delaunay Trian
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a a b d Voronoi Diagrams and Delaun
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Documenta Math. 433 Around Hilbert
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Around Hilbert’s 17th Problem 435
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Around Hilbert’s 17th Problem 437
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Documenta Math. 439 From Kepler to
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From Kepler to Hales 441 Figure 1:
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From Kepler to Hales 443 assertions
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From Kepler to Hales 445 |- !A. con
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Documenta Math. 447 Vilfredo Pareto
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Vilfredo Pareto and Multi-objective
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Documenta Math. 455 Optimisation an
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Optimisation and Utility Functions
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Optimisation and Utility Functions
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