抽象凸分析(英文)/国外优秀数学著作原版系列
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作者(罗)伊凡·辛格|责编:王勇钢//李兰静
出版社哈尔滨工业大学
ISBN9787560391557
出版时间2020-11
装帧平装
开本其他
定价68元
货号31091737
上书时间2024-08-10
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目录
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 □(数理化公式) Where X
Is a Set
2.3 An Equivalent Approach, via Separation by Functions:
W-Convexity of Subsets of a Set X, Where □(数理化公式)
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 □(数理化公式)
2.6 (W, □(数理化公式))-Convexity of Subsets of a Set X, Where W Is a Set and
□(数理化公式)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 □(数理化公式)
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□(数理化公式)
内容摘要
本书主要包括从凸分析到抽象凸分析、一个完整格
的元素的抽象凸性、集合子集的抽象凸性、集上函数的抽象凸性、.晶格之间的对偶性、晶格族之间的对偶、函数集合之间的对偶性、
抽象的次微分等内容，也包含了关于当代抽象凸分析.先进且详尽的考查。本书致力于研究通过在一个有序的空间中取得上确界（或下确界）元素族的操作来表示复杂的对象。在本书中，读者可以找到对抽象凸性的几种方法的介绍和它们之间的比较。本书适合对抽象凸分析感兴趣的数学专业学生及教师参考阅读。
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