Convex functions

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Front Cover ; Convex Functions ; Copyright Page ; Contents ; Preface ; Acknowledgments ; Introduction ; List of Notation ; Chapter I. Convex Functions on the Real Line ; 10. Introduction ; 11. Continuity and Differentiability ; 12. Characterizations. 13. Closure under Functional Operations 14. Differences of Convex Functions ; 15. Conjugate Convex Functions ; Chapter II. Normed Linear Spaces ; 20. Introduction ; 21. Normed Linear Spaces ; 22. Functions on Normed Linear Spaces ; 23. Derivatives in a Normed Linear Space. Chapter III. Convex Sets 30. Introduction ; 31. Convex Sets and Affine Sets ; 32. Hyperplanes and Extreme Points ; Chapter IV. Convex Functions on a Normed Linear Space ; 40. Introduction ; 41. Continuity of Convex Functions ; 42. Differentiable Convex Functions. 43. The Support of Convex Functions 44. Differentiability of Convex Functions ; Chapter V. Optimization ; 50. Introduction ; 51. Maxima and Minima ; 52. Minimax Theorems and the Theory of Games ; 53. Linear Programming ; 54. The Simplex Method ; 55. Convex Programming. 56. Approximation Chapter VI. Inequalities ; 60. Introduction ; 61. The Classical Inequalities ; 62. The Generalized Geometric Mean-Arithmetic Mean Inequality and Norms; 63. Matrix Inequalities ; Chapter VII. Midconvex Functions ; 70. Introduction ; 71. Midconvex Functions on a Normed Linear Space