Convex Analysis

R. Tyrrell Rockafellar

Princeton University Press, Jan 12, 1997 - 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.

Contents

• IV: 3
• V: 10
• VI: 16
• VII: 23
• VIII: 29
• X: 37
• XI: 39
• XIII: 45
• XIV: 54
• XVI: 66
• XVII: 76
• XIX: 87
• XX: 89
• XXI: 96
• XXIII: 106
• XXIV: 115
• XXVI: 122
• XXVIII: 134
• XXX: 145
• XXXI: 147
• XXXII: 156
• XXXIV: 164
• XXXV: 173
• XXXVII: 179
• XXXIX: 192
• XLI: 205
• XLII: 207
• XLIV: 221
• XLVI: 235
• XLVIII: 245
• L: 255
• LI: 257
• LIII: 267
• LV: 285
• LVII: 301
• LIX: 321
• LXI: 336
• LXIII: 341
• LXIV: 343
• LXVI: 353
• LXVIII: 364
• LXX: 373
• LXXI: 382
• LXXIII: 393
• LXXIV: 395
• LXXVI: 407
• LXXVII: 419
• LXXVIII: 427
• LXXIX: 441

Bibliographic information

• Title: Convex Analysis; Volume 28 of Princeton Landmarks in Mathematics and Physics; Issue 28 of Princeton Mathematical Series, ISSN 0079-5194; Princeton paperbacks
• Author: R. Tyrrell Rockafellar
• Edition: reprint, revised
• Publisher: Princeton University Press, 1997
• ISBN: 0691015864, 9780691015866
• Length: 451 pages
• Subjects: Mathematics / Calculus; Mathematics / General; Mathematics / Geometry / General; Mathematics / Mathematical Analysis; Mathematics / Optimization