Convex Analysis

Front Cover
Princeton University Press, 1970 - Mathematics - 451 pages

Available for the first time in paperback, R. Tyrrell Rockafellar's classic study presents readers with a coherent branch of nonlinear mathematical analysis that is especially suited to the study of optimization problems. Rockafellar's theory differs from classical analysis in that differentiability assumptions are replaced by convexity assumptions. The topics treated in this volume include: systems of inequalities, the minimum or maximum of a convex function over a convex set, Lagrange multipliers, minimax theorems and duality, as well as basic results about the structure of convex sets and the continuity and differentiability of convex functions and saddle- functions.


This book has firmly established a new and vital area not only for pure mathematics but also for applications to economics and engineering. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient background for this book. There is also a guide for the reader who may be using the book as an introduction, indicating which parts are essential and which may be skipped on a first reading.

 

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Contents

IV
3
V
10
VI
16
VII
23
VIII
29
X
37
XI
39
XII
45
XXXVIII
205
XXXIX
207
XLI
221
XLIII
235
XLV
245
XLVI
255
XLVII
257
XLVIII
267

XIII
54
XIV
66
XVI
76
XVIII
87
XIX
89
XX
96
XXII
106
XXIV
115
XXVI
122
XXVII
134
XXVIII
145
XXIX
147
XXX
156
XXXII
164
XXXIII
173
XXXV
179
XXXVII
192
L
285
LII
301
LIV
321
LVI
336
LVIII
341
LIX
343
LX
353
LXI
364
LXIII
373
LXIV
382
LXVI
393
LXVII
395
LXIX
407
LXX
419
LXXI
427
LXXII
441
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About the author (1970)

R. Tyrrell Rockafellar is Professor of Mathematics and Applied Mathematics at the University of Washington-Seattle. For his work in convex analysis and optimization, he was awarded the Dantzig Prize by the Society for Industrial and Applied Mathematics and the Mathematical Programming Society.

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