《離散與微分包含的逼近和最佳化》是2015-8-1出版的圖書，作者是馬哈茂多夫。
基本介紹
- 書名：離散與微分包含的逼近和最佳化
- 作者：馬哈茂多夫
- 出版時間：2015-8-1
基本信息,內容提要,目錄,
基本信息
書名：離散與微分包含的逼近和最佳化
作者： 馬哈茂多夫 責編：張永芹
I S B N：978-7-5603-5520-7 定價：58.00
出版日期：2015-8-1 開本：16
所屬叢書： 頁數：395
圖書分類：Q.數學類 中圖分類：O數理科學和化學
內容提要
本書英文影印版由 Elsevier (Singapore) Pte Ltd. 授權哈爾濱工業大學出版社在中國大陸境內獨家發行。本版僅限在中國境內(不包括香港、澳門以及台灣)出版及標價銷售。未經許可之出口，視為違反著作權法，將受民事及刑事法律之制裁。
目錄
Dedication
Preface
Acknowledgments
About the Author
1 Convex Sets and Functions//1
1.1 Introduction//1
1.2 Some Basic Properties of Convex Sets//3
1.3 Convex Cones and Dual Cones//14
1.4 The Main Properties of Convex Functions//25
1.5 Conjugate of Convex Function//36
1.6 Directional Derivatives and Subdifferentials//41
2 Multivalued Locally Adjoint Mappings//53
2.1 Introduction//53
2.2 Locally Adjoint Mappings to Convex Multivalued Mappings//55
2.3 The Calculus of Locally Adjoint Mappings//64
2.4 Locally Adjoint Mappings in Concrete Cases//72
2.5 Duality Theorems for Convex Multivalued Mappings//86
3 Mathematical Programming and Multivalued Mappings//93
3.1 Introduction//93
3.2 Necessary Conditions for an Extremum in Convex Programming Problems//97
3.3 Lagrangian and Duality in Convex Programming Problems//107
3.4 Cone of Tangent Directions and Locally Tents//117
3.5 CUA of Functions//122
3.6 LAM in the Nonconvex Case//127
3.7 Necessary Conditions for an Extremum in Nonconvex Problems//133
4 Optimization of Ordinary Discrete and Differential Inclusions and
-Transversality Conditions//143
4.1 Introduction//143
4.2 Optimization of Ordinary Discrete Inclusions//149
4.3 Polyhedral Optimization of Discrete and Differential Inclusions//156
4.4 Polyhedral Adjoint Differential Inclusions and the Finiteness of Switching Numbers//170
4.5 Bolza Problems for Differential Inclusions with State Constraints//181
4.6 Optimal Control of Hereditary Functional-Differential Inclusions with Varying Time Interval and State Constraints//188
4.7 Optimal Control of HODI of Bolza Type with Varying Time Interval//206
5 On Duality of Ordinary Discrete and Differential Inclusions
with Convex Structures//217
5.1 Introduction//217
5.2 Duality in Mathematical Programs with Equilibrium Constraints//219
5.3 Duality in Problems Governed by Polyhedral Maps//226
5.4 Duality in Problems Described by Convex Discrete Inclusions//235
5.5 The Main Duality Results in Problems with Convex Differential
Inclusions//245
6 Optimization of Discrete and Differential Inclusions with
Distributed Parameters via Approximation//253
6.1 Introduction//253
6.2 The Optimality Principle of Boundary-Value Problems for Discrete-Approximation and First-Order Partial Differential Inclusions and Duality//257
6.3 Optimal Control of the Cauchy Problem for First-Order Discrete
and Partial Differentia1 Inclusions//274
6.4 Optimal Control of Darboux-Type Discrete-Approximation and Differential Inclusions with Set -Valued Boundary Conditions and Duality//289
6.5 Optimal Control of the Elliptic-Type Discrete and Differential Inclusions with Dirichlet and Neumann Boundary Conditions via Approximation//312
6.6 Optimization of Discrete-Approximation and Differential Inclusions of Parabolic Type and Duality//338
6.7 Optimization of the First Boundary Value Problem for Hyperbolic-Type Discrete-Approximation and Differential Inclusions//347
References//365
Glossary of Notations//377
