Linear Programming and Extensions

Couverture
Princeton University Press, 1998 - 627 pages

In real-world problems related to finance, business, and management, mathematicians and economists frequently encounter optimization problems. In this classic book, George Dantzig looks at a wealth of examples and develops linear programming methods for their solutions. He begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them. Treatments of the price concept, the transportation problem, and matrix methods are also given, and key mathematical concepts such as the properties of convex sets and linear vector spaces are covered.

George Dantzig is properly acclaimed as the "father of linear programming." Linear programming is a mathematical technique used to optimize a situation. It can be used to minimize traffic congestion or to maximize the scheduling of airline flights. He formulated its basic theoretical model and discovered its underlying computational algorithm, the "simplex method," in a pathbreaking memorandum published by the United States Air Force in early 1948. Linear Programming and Extensions provides an extraordinary account of the subsequent development of his subject, including research in mathematical theory, computation, economic analysis, and applications to industrial problems.

Dantzig first achieved success as a statistics graduate student at the University of California, Berkeley. One day he arrived for a class after it had begun, and assumed the two problems on the board were assigned for homework. When he handed in the solutions, he apologized to his professor, Jerzy Neyman, for their being late but explained that he had found the problems harder than usual. About six weeks later, Neyman excitedly told Dantzig, "I've just written an introduction to one of your papers. Read it so I can send it out right away for publication." Dantzig had no idea what he was talking about. He later learned that the "homework" problems had in fact been two famous unsolved problems in statistics.

 

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Table des matières

II
1
III
6
IV
7
V
10
VI
12
VII
16
VIII
20
IX
28
LXVI
277
LXVII
286
LXVIII
291
LXIX
297
LXX
299
LXXI
300
LXXII
308
LXXIII
314

X
32
XI
34
XII
35
XIII
42
XIV
50
XV
55
XVI
57
XVII
60
XVIII
62
XIX
69
XX
75
XXI
81
XXII
84
XXIII
85
XXIV
89
XXV
94
XXVI
100
XXVII
111
XXVIII
120
XXIX
123
XXX
128
XXXI
134
XXXII
140
XXXIII
144
XXXIV
147
XXXV
156
XXXVI
160
XXXVII
166
XXXVIII
173
XXXIX
177
XL
183
XLI
189
XLII
195
XLIII
202
XLIV
210
XLVI
211
XLVII
217
XLVIII
221
XLIX
226
L
228
LII
231
LIII
237
LIV
240
LV
241
LVI
243
LVII
245
LVIII
247
LIX
252
LX
253
LXI
254
LXII
260
LXIII
264
LXIV
265
LXV
275
LXXIV
316
LXXV
322
LXXVI
330
LXXVII
332
LXXVIII
335
LXXIX
342
LXXX
346
LXXXI
351
LXXXII
352
LXXXIII
357
LXXXIV
361
LXXXV
366
LXXXVI
368
LXXXVII
377
LXXXVIII
383
LXXXIX
385
XC
398
XCI
403
XCII
404
XCIII
405
XCIV
411
XCV
413
XCVI
420
XCVII
424
XCVIII
431
XCIX
433
C
440
CI
446
CII
448
CIII
455
CIV
462
CV
466
CVI
469
CVII
471
CVIII
479
CIX
482
CX
490
CXI
497
CXII
499
CXIII
503
CXIV
507
CXV
511
CXVI
514
CXVII
521
CXVIII
535
CXX
551
CXXI
557
CXXII
566
CXXIII
568
CXXIV
580
CXXV
589
CXXVI
614
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À propos de l'auteur (1998)

George B. Dantzig is Professor Emeritus in the Department of Engineering-Economic Systems and Operations Research at Stanford University.

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