Convex Optimization, Part 1

Front Cover
Cambridge University Press, Mar 8, 2004 - Business & Economics - 716 pages
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
 

Contents

II
1
IV
4
V
7
VI
9
VII
11
VIII
14
IX
16
X
19
LXVI
397
LXVII
402
LXVIII
405
LXIX
410
LXX
416
LXXI
422
LXXII
432
LXXIII
438

XI
21
XIII
27
XIV
35
XV
43
XVI
46
XVII
51
XVIII
59
XIX
60
XX
67
XXI
79
XXII
90
XXIII
95
XXIV
104
XXV
108
XXVI
112
XXVII
113
XXVIII
127
XXX
136
XXXI
146
XXXII
152
XXXIII
160
XXXIV
167
XXXV
174
XXXVI
188
XXXVII
189
XXXVIII
215
XL
223
XLI
232
XLII
237
XLIII
241
XLIV
249
XLV
253
XLVI
258
XLVII
264
XLVIII
272
XLIX
273
L
289
LI
291
LIII
302
LIV
305
LV
318
LVI
324
LVII
343
LVIII
344
LIX
351
LX
359
LXI
364
LXII
374
LXIII
384
LXIV
392
LXV
393
LXXIV
446
LXXV
447
LXXVI
455
LXXVII
457
LXXIX
463
LXXX
466
LXXXI
475
LXXXII
484
LXXXIII
496
LXXXIV
508
LXXXV
513
LXXXVI
514
LXXXVII
521
LXXXVIII
525
LXXXIX
531
XC
542
XCI
556
XCII
557
XCIII
561
XCV
562
XCVI
568
XCVII
579
XCVIII
585
XCIX
596
C
609
CI
615
CII
621
CIII
623
CIV
631
CV
633
CVI
637
CVII
639
CVIII
640
CIX
645
CX
652
CXI
653
CXII
655
CXIII
656
CXIV
657
CXV
659
CXVI
661
CXVII
664
CXVIII
668
CXIX
672
CXX
681
CXXI
684
CXXII
685
CXXIII
697
CXXIV
701
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About the author (2004)

Lieven Vandenberghe received his PhD from the Katholieke Universiteit, Leuven, Belgium, and is a Professor of Electrical Engineering at the University of California, Los Angeles. He has published widely in the field of optimization and is the recipient of a National Science Foundation CAREER award.