出版时间：2011-1 出版社：世界图书出版公司 作者：洛克菲拉 页数：451
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.
Preface .Introductory Remarks: a Guide for the ReaderPART l: BASIC CONCEPTS1. Affine Sets2. Convex Sets and Cones3. The Algebra of Convex Sets4. Convex Functions5. Functional OperationsPART II: TOPOLOGICAL PROPERTIES6. Relative Interiors of Convex Sels7. Closures of Convex Functions8. Recession Cones and Unboundedness9. Some CIosedness Criteria10. Continuity of Convex FunctionsPART Ⅲ: DUALITY CORRESPONDENCES11. Separation Theorems12. Conjugates of Convex Functions13. Support Furctions14. Polars of Convex Sets15. Polars of Convex Functions16.Dual OperationsPART IV: REPRESENTATION AND INEQUALITIES17. Carath6odory's Theorem18. Extreme Points and Faces of Convex Sets19. Polyhedral Convex Sets and Functions20. Some Applications of Polyhedral Convexity21.Helly's Theorem and Systems of Inequalities22. Linear InequalitiesCONTENTSPART V: DIFFERENTIAL THEORY23. Directional Derivatives and Subgradients24. Differential Continuity and Monotonicity25. Differentiability of Convex Functions26. The Legendre TransformationPART VI: CONSTRAINED EXTREMUM PROBLEMS27. The Minimum of a Convex Function28. Ordinary Convex Programs and Lagrange Multipliers29. Bifunctions and Generalized Convex Programs30. Adjoint Bifunctions and Dual Programs 31. Fenchel's Duality Theorem32. The Maximum of a Convex FunctionPART VII:' SADDLE-FUNCTIONS AND MINIMAX THEORY33. Saddle-Functions34. Closures and Equivalence Classes35. Continuity and Differentiability of Saddle-functions36. Minimax Problems37. Conjugate Saddle-functions and Minimax TheoremsPART VIII: CONVEX ALGEBRA38. The Algebra of Bifunctions39. Convex Processes .Comments and ReferencesBibliographyIndex