凸分析（英文版）
出版时间：2011年版
内容简介
　　convexity has been increasingly important in recent years in the study of extremum problems in many areas of applied mathematics. the purpose of this book is to provide an exposition of the theory of convex sets and functions in which applications to extremum problems play the central role.systems of inequalities， the minimum or maximum of a convex function over a convex set， lagrange multipliers， and minimax theorems are among the topics treated， as well as basic results about the structure of convex sets and the continuity and differentiability of convex functions and saddle-functions. duality is emphasized throughout， particularly in the form of fenchers conjugacy correspondence for convex functions.
目录
preface
introductory remarks: a guide for the reader
part i: basic concepts
　1. affine sets*
　2. convex sets and cones
　3. the algebra of convex sets
　4. convex functions
　5. fubctional operations
part ii: topological properties
　6. relative interiors of conyex sets
　7. closures of convex functions
　8. recession cones and unboundedness
　9. some closedness criteria
　10. continuity of convex functions
part iii: duality correspondences
　11. separation theorems
　12. conjugates of convex functions
　13. support functions
　14. polars of convex sets
　15. polars of convex functions
　16. dual operations
part iv: representation and inequalities
　17. caratheodory's theorem
　18. extreme points and faces of convex sets
　19. polyhedral convex sets and functions
　20. some applications of polyhedral convexity
　21. helly's theorem and systems of inequalities
　22. linear inequalities
part v: differential theory
　23. directional derivatives and subgradients
　24. differential continuity and monotonicity
　25. differentiability of convex functions
　26. the legendre transformation
part vi: constrained extremum problems
　27. the minimum of a convex function
　28. ordinary convex programs and lagrange multipliers
　29. bifunctions and generalized convex programs
　30. adjoint bifunctions and dual programs
　31. fenchel's duality theorem
　32. the maximum of a convex function
part vii:saddle-functions and minimax theory
　33. saddle-functions
　34. closures and equivalence classes
　35. continuity and differentiability of saddle-functions
　36. minimax problems
　37. conjugate saddle-functions and minimax theorems
part viii: convex algebra
　38. the algebra of bifunctions
　39. convex processes
comments and references
bibliography
index