Documenta Mathematica Optimization Stories - Mathematics

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30 Peter Deuflhard [10] I. Newton. Philosophiae naturalis principia mathematica. Colonia Allobrogum: sumptibus Cl. et Ant. Philibert, 1760. [11] J.M. Ortega and W.C. Rheinboldt. Iterative Solution of Nonlinear Equations in Several Variables. Classics in Appl. Math. SIAM Publications, Philadelphia, 2nd edition, 2000. [12] D.T. Whiteside. The Mathematical Papers of Isaac Newton (7 volumes), 1967–1976. [13] T.J. Ypma. Historical Development of the Newton-Raphson Method. SIAM Rev., 37:531–551, 1995. Peter Deuflhard Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB) Takustraße 7 14195 Berlin Germany deuflhard@zib.de Documenta Mathematica · Extra Volume ISMP (2012) 25–30
Documenta Math. 31 Euler and Infinite Speed Eberhard Knobloch 2010 Mathematics Subject Classification: 01A50, 70-03 Keywords and Phrases: Euler, Galileo, Maupertuis, tunnel through the earth, damped oscillation ThefamousSwissmathematicianLeonhardEulerwasborninBaselonthe15th of April 1707. Already in 1720 when he was still a thirteen-year-old boy, he enrolled at the University of Basel. One year later, he obtained the Bachelor’s degree. In 1723 when he was sixteen years old, he obtained his Master’s degree (A. L. M. = Master of Liberal Arts). In 1727 without ever having obtained the Ph. D. degree he submitted a short habilitation thesis (consisting of fifteen pages); that is, a thesis in application for the vacant professorship of physics at the University of Basel. At that time he had published two papers, one of them being partially faulty. No wonder that the commission which looked for a suitable candidate for the professorship did not elect him. Yet Euler was very much infuriated by this decision. Still in 1727, he went to St. Petersburg in order to work at the newly founded Academy of Sciences. He never came back to Switzerland. Between 1741 and 1766 he lived and worked in Berlin at the reformed Academy of Sciences and Literature of Berlin. In 1766 he returned to St. Petersburg where he died on the 18th of September 1783. The complete title of his habilitation thesis reads: May it bring you happiness and good fortune – Physical dissertation on sound which Leonhard Euler, Master of the liberal arts submits to the public examination of the learned in the juridical lecture-room on February 18, 1727 at 9 o’clock looking at the free professorship of physics by order of the magnificent and wisest class of philosophers whereby the divine will is nodding assent. The most eminent young man Ernst Ludwig Burchard, candidate of philosophy, is responding. As we know, all imploring was in vain: Euler did not get the position. The thesisisallthemoreinterestingbecauseEulerhadaddedasupplementinwhich he formulated six statements regarding utterly different subjects. For example he maintained that Leibniz’s theory of preestablished harmony between body Documenta Mathematica · Extra Volume ISMP (2012) 31–35
Page 1 and 2: Documenta Mathematica Journal der D
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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 83 and 84: 2 A first counterexample Who Solved
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Who Solved the Hirsch Conjecture? 8
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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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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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