Optimization Theory with Applications

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Courier Corporation, 1969 - Technology & Engineering - 612 pages
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Optimization principles are of undisputed importance in modern design and system operation. They can be used for many purposes: optimal design of systems, optimal operation of systems, determination of performance limitations of systems, or simply the solution of sets of equations. While most books on optimization are limited to essentially one approach, this volume offers a broad spectrum of approaches, with emphasis on basic techniques from both classical and modern work.
After an introductory chapter introducing those system concepts that prevail throughout optimization problems of all types, the author discusses the classical theory of minima and maxima (Chapter 2). In Chapter 3, necessary and sufficient conditions for relative extrema of functionals are developed from the viewpoint of the Euler-Lagrange formalism of the calculus of variations. Chapter 4 is restricted to linear time-invariant systems for which significant results can be obtained via transform methods with a minimum of computational difficulty. In Chapter 5, emphasis is placed on applied problems which can be converted to a standard problem form for linear programming solutions, with the fundamentals of convex sets and simplex technique for solution given detailed attention. Chapter 6 examines search techniques and nonlinear programming. Chapter 7 covers Bellman's principle of optimality, and finally, Chapter 8 gives valuable insight into the maximum principle extension of the classical calculus of variations.
Designed for use in a first course in optimization for advanced undergraduates, graduate students, practicing engineers, and systems designers, this carefully written text is accessible to anyone with a background in basic differential equation theory and matrix operations. To help students grasp the material, the book contains many detailed examples and problems, and also includes reference sections for additional reading.

 

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Contents

I
1
II
3
III
5
IV
7
V
8
VI
18
VII
19
VIII
22
LIII
234
LIV
239
LV
254
LVI
264
LVII
266
LVIII
272
LIX
287
LX
292

IX
24
X
26
XI
29
XII
30
XIII
31
XIV
35
XV
36
XVI
42
XVII
43
XVIII
45
XIX
47
XX
51
XXI
62
XXII
64
XXIII
68
XXIV
75
XXV
82
XXVI
87
XXVII
90
XXVIII
91
XXIX
100
XXX
104
XXXI
118
XXXII
123
XXXIII
124
XXXIV
135
XXXV
136
XXXVI
141
XXXVII
144
XXXVIII
150
XXXIX
162
XL
170
XLI
173
XLII
182
XLIII
193
XLIV
194
XLV
195
XLVI
200
XLVII
204
XLVIII
209
XLIX
215
L
224
LI
227
LII
232
LXI
296
LXII
309
LXIII
314
LXIV
322
LXV
331
LXVI
333
LXVII
345
LXVIII
350
LXIX
367
LXX
369
LXXI
378
LXXIII
380
LXXIV
386
LXXV
394
LXXVI
402
LXXVII
404
LXXVIII
408
LXXIX
418
LXXX
423
LXXXI
431
LXXXII
440
LXXXIII
450
LXXXIV
452
LXXXV
462
LXXXVI
478
LXXXVII
479
LXXXVIII
481
LXXXIX
485
XC
486
XCI
493
XCII
500
XCIII
513
XCIV
523
XCV
525
XCVI
536
XCVII
539
XCVIII
555
XCIX
566
C
572
CI
580
CII
593
CIII
599
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