Linear and Nonlinear Programming: Second Edition (Google eBook)

Front Cover
Springer Science & Business Media, Sep 30, 2003 - Business & Economics - 491 pages
4 Reviews

"Linear and Nonlinear Programming" is considered a classic textbook in Optimization. While it is a classic, it also reflects modern theoretical insights. These insights provide structure to what might otherwise be simply a collection of techniques and results, and this is valuable both as a means for learning existing material and for developing new results. One major insight of this type is the connection between the purely analytical character of an optimization problem, expressed perhaps by properties of the necessary conditions, and the behavior of algorithms used to solve a problem. This was a major theme of the first edition of this book and the second edition expands and further illustrates this relationship.

"Linear and Nonlinear Programming" covers the central concepts of practical optimization techniques. It is designed for either self-study by professionals or classroom work at the undergraduate or graduate level for technical students. Like the field of optimization itself, which involves many classical disciplines, the book should be useful to system analysts, operations researchers, numerical analysts, management scientists, and other specialists from the host of disciplines from which practical optimization applications are drawn.

  

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Contents

I
xv
II
1
III
2
IV
7
V
13
VI
14
VII
17
VIII
22
LXXVI
264
LXXVII
267
LXXVIII
271
LXXIX
275
LXXX
278
LXXXI
283
LXXXII
284
LXXXIII
291

IX
26
X
32
XI
36
XII
40
XIII
44
XIV
49
XV
54
XVI
55
XVII
61
XVIII
64
XIX
71
XX
72
XXI
81
XXIII
84
XXIV
86
XXV
91
XXVI
93
XXVII
95
XXVIII
100
XXIX
106
XXX
113
XXXII
117
XXXIII
119
XXXIV
122
XXXV
129
XXXVI
130
XXXVII
133
XXXVIII
137
XXXIX
145
XL
153
XLI
154
XLII
163
XLIII
170
XLIV
172
XLV
176
XLVI
178
XLVII
185
XLVIII
189
XLIX
190
L
192
LI
193
LII
196
LIII
203
LIV
205
LV
207
LVI
210
LVII
216
LVIII
221
LIX
223
LX
226
LXI
227
LXII
228
LXIII
234
LXVI
237
LXVII
239
LXVIII
242
LXIX
244
LXX
248
LXXI
250
LXXII
253
LXXIII
256
LXXIV
259
LXXV
261
LXXXIV
293
LXXXV
296
LXXXVI
297
LXXXVII
302
LXXXVIII
304
LXXXIX
308
XC
310
XCI
314
XCII
318
XCIII
319
XCIV
322
XCV
326
XCVI
333
XCVII
341
XCVIII
346
XCIX
353
C
355
CI
356
CII
361
CIV
362
CV
365
CVI
367
CVII
374
CVIII
376
CIX
378
CX
380
CXI
383
CXII
387
CXIII
388
CXIV
392
CXVI
393
CXVII
398
CXVIII
399
CXIX
402
CXX
407
CXXI
412
CXXII
414
CXXIII
416
CXXIV
417
CXXV
419
CXXVIII
423
CXXIX
429
CXXX
431
CXXXI
435
CXXXII
440
CXXXIII
442
CXXXIV
445
CXXXV
446
CXXXVI
451
CXXXIX
452
CXL
453
CXLI
454
CXLII
455
CXLIII
456
CXLIV
460
CXLV
461
CXLVI
464
CXLVII
466
CXLVIII
468
CL
472
CLI
483
Copyright

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Popular passages

Page 17 - C such that x = nx\ + (1 a)z2 for some a (0, 1). An extreme point is thus a point that does not lie strictly within the line segment connecting two other points in the set.
Page 15 - Given a linear program in standard form (5.1.1) where A is an mxn matrix of rank m, i) if there is a feasible solution, there is a basic feasible solution; ii) if there is an optimal feasible solution, there is an optimal basic feasible solution. Proof of (i): Denote the columns of A by ai,tt2, ,an and let z = (xi,X2,- ,xn)T be a feasible solution.

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About the author (2003)

David G. Luenberger has directed much of his career toward teaching "portable concepts" - organizing theory around concepts and actually "porting" the concepts to applications where, in the process, the general concepts are often discovered. The search for fundamentals has explicitly directed his research in the fields of control, optimization, planning, economics, and investments, and in turn, it is the discovery of these fundamentals that have motivated his textbook writing projects.

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