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抽象凸分析:英文 版權信息
- ISBN：9787560391557
- 條形碼：9787560391557 ; 978-7-5603-9155-7
- 裝幀：一般膠版紙
- 冊數：暫無
- 重量：暫無
- 所屬分類：>>
抽象凸分析:英文 內容簡介
《抽象凸分析（英文）》主要包括從凸分析到抽象凸分析、一個完整格的元素的抽象凸性、集合子集的抽象凸性、集上函數的抽象凸性、完全晶格之間的對偶性、晶格族之間的對偶、函數集合之間的對偶性、抽象的次微分等內容，也包含了關于當代抽象凸分析非常先進且詳盡的考查。 《抽象凸分析（英文）》致力于研究通過在一個有序的空間中取得上確界（或下確界）元素族的操作來表示復雜的對象。 在《抽象凸分析（英文）》中，讀者可以找到對抽象凸性的幾種方法的介紹和它們之間的比較。 《抽象凸分析（英文）》適合對抽象凸分析感興趣的數學專業學生及教師參考閱讀。
抽象凸分析:英文 目錄
Foreword
Preface
Introduction: From Convex Analysis to Abstract Convex Analysis
0.1 Abstract Convexity of Sets
0.1a Inner Approaches
0.1b Intersectional and Separational Approaches
0.1c Approaches via Convexity Systems and Hull Operators
0.2 Abstract Convexity of Functions
0.3 Abstract Convexity of Elements of Complete Lattices
0.4 Abstract Quasi-Convexity of Functions
0.5 Dualities
0,6 Abstract Conjugations
0.7 Abstract Subdifferentials
0.8 Some Applications of Abstract Convex Analysis to Optimization
Theory
0.Sa Applications to Abstract Lagrangian Duality
0.8b Applications to Abstract Surrogate Duality
Chapter One Abstract Convexity of Elements of a Complete Lattice
1.1 The Main (Supremal) Approach: M-Convexity of Elements of a
Complete Lattice E, Where M c E
1.2 lnfimal and Supremal Generators and M-Convexity
1.3 An Equivalent Approach: Convexity Systems
1.4 Another Equivalent Approach: Convexity with Respect to a Hull
Operator
Chapter Two Abstract Convexity of Subsets of a Set
2.1 M-Convexity of Subsets of a Set X, Where M c 2x
2.2 Some Particular Cases
2.2a Convex Subsets of a Linear Space X
2.2b Closed Convex Subsets of a Locally Convex Space X
2.2c Evenly Convex Subsets of a Locally Convex Space X
2.2d Closed Affine Subsets of a Locally Convex Space X
2.2e Evenly Coaffine Subsets of a Locally Convex Space X
2.2f Spherically Convex Subsets of a Metric Space X
2.2g Closed Subsets of a Topological Space X
2.2h Order Ideals and Order Convex Subsets of a Poset X
2.2i Parametrizations of Families □(數理化公式) Where X
Is a Set
2.3 An Equivalent Approach, via Separation by Functions:
W-Convexity of Subsets of a Set X, Where □(數理化公式)
2.4 A Particular Case: Closed Convex Sets Revisited
2.5 Other Concepts of Convexity of Subsets of a Set X, with Respect
to a Set of Functions □(數理化公式)
2.6 (W, □(數理化公式))-Convexity of Subsets of a Set X, Where W Is a Set and
□(數理化公式)R Is a Coupling Function
Chapter Three Abstract Convexity of Functions on a Set
3.1 W-Convexity of Functions on a Set X, Where □(數理化公式)
3.2 Some Particular Cases
3.2a C(X* + R), Where X Is a Locally Convex Space
3.2b C(X*), Where X Is a Locally Convex Space
3.2c The Case Where X = {0, 1}n and W□(數理化公式)
3.2d The Case Where X = {0, 1}n and W □(數理化公式)
3.2e ot-Ho1der Continuous Functions with Constant N,
Where0 □(數理化公式)
3.2f Suprema of Ho1der Continuous Functions, Where
□(數理化公式)
3.2g The Case Where □(數理化公式)
3.3 (W, →o)-ConvexityofFunctions on a Set X, Where W Is a Set and
□(數理化公式)R Is a Coupling Function
Chapter Four Abstract Quasi-Convexity of Functions on a Set
4.1 M-Quasi-Convexity of Functions on a Set X, Where □(數理化公式)
4.2 Some Particular Cases
4.2a Quasi-Convex Functions on a Linear Space X
4.2b Lower Semicontinuous Quasi-Convex Functions on a
Locally Convex Space X
4.2c Evenly Quasi-Convex Functions on a Locally Convex
Space X
4.2d Evenly Quasi-Coaffine Functions on a Locally Convex
Space X
4.2e Lower Semicontinuous Functions on a Topological
Space X
4.2f Nondecreasing Functions on a Poset X
4.3 An Equivalent Approach: W-Quasi-Convexity of Functions on a
□(數理化公式)
4.4 Relations Between W-Convexity and W-Quasi-Convexity of
Functions on a Set X, Where W □(數理化公式)
4.5 Some Particular Cases
4.5a Lower Semicontinuous Quasi-Convex Functions
Revisited
4.5b Evenly Quasi-Convex Functions Revisited
4.5c Evenly Quasi-Coaffine Functions Revisited
4.6 (W, →0)-Quasi-Convexity of Functions on a Set X, Where W Is a
Set and □(數理化公式) : X x W → R Is a Coupling Function
4.7 Other Equivalent Approaches: Quasi-Convexity of Functions on
a Set X, with Respect to Convexity Systems/3 c 2x and Hull
Operators u : 2x → 2x
4.8 Some Characterizations of Quasi-Convex Hull Operators
among Hull Operators on □(數理化公式)
Chapter Five Dualities Between Complete Lattices
5.1 Dualities and lnfimal Generators
5.2 Duals of Dualities
5.3 Relations Between Dualities and M-Convex Hulls
5.4 Partial Order and Lattice Operations for Dualities
Chapter Six Dualities Between Families of Subsets
6.1 DualitiesA :2x → 2w, Where X and W Are Two Sets
6.2 Some Particular Cases
6.2a Some Minkowski-Type Dualities
6.2b Some Dualities Obtained from the Minkowski-Type
Dualities AM, by Parametrizing the Family M
6.3 Representations of Dualities A : 2x → 2w with the Aid of
Subsets □(數理化公式) of X → W and Coupling Functions □(數理化公式) : X → W →
6.4 Some Particular Cases
6.4a Representations with the Aid of Subsets f2 of X X W
6.4b Representations with the Aid of Coupling Functions
□(數理化公式)
Chapter Seven Dualities Between Sets of Functions
7.1 Dualities A □(數理化公式) Where X and W Are Two Sets
7.2 Representations of Dualities A : Ax → F, Where X Is a Set
and □(數理化公式) and F Are Complete Lattices
7.3 Dualities A : Ax → Bw, Where X Is a Set and (A,
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