Convex analysis
著者
書誌事項
Convex analysis
（Princeton landmarks in mathematics and physics）（Princeton paperbacks）
Princeton University Press, 1997, c1970
- : pbk
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注記
"Tenth pringing and first paperback printing in the Princeton Landmarks in Mathematics and Physics series, 1997"--T.p. verso
Bibliography: p. 433-446
Includes index
内容説明・目次
内容説明
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.
目次
*Frontmatter, pg. i*Preface, pg. vii*Contents, pg. ix*Introductory Remarks: A Guide Jar the Reader, pg. xi*Part I. Basic Concepts, pg. 1*Part II. Topological Properties, pg. 41*Part III. Duality Correspondences, pg. 93*Part IV. Representation and Inequalities, pg. 151*Part V. Differential Theory, pg. 211*Part VI. Constrained Extremum Problems, pg. 261*Part VII. Saddle-Functions and Minimax Theory, pg. 347*Part VIII. Convex Algebra, pg. 399*Comments and References, pg. 425*Bibliography, pg. 433*Index, pg. 447
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