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
30
X
34
XI
34
XII
34
XXXIV
209
XXXVI
223
XXXVII
233
XXXVIII
243
XXXIX
245
XL
255
XLII
273
XLIII
289

XIV
54
XVI
64
XVIII
75
XIX
77
XX
84
XXI
103
XXII
110
XXIII
122
XXIV
133
XXV
135
XXVI
144
XXVIII
161
XXX
167
XXXI
180
XXXII
193
XXXIII
195
XLV
309
XLVII
324
XLIX
329
L
331
LI
341
LIII
352
LV
361
LVI
370
LVIII
381
LIX
383
LXI
395
LXII
407
LXIII
415
LXIV
429
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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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