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變分分析 版權信息
- ISBN：9787510061363
- 條形碼：9787510061363 ; 978-7-5100-6136-3
- 裝幀：一般膠版紙
- 冊數：暫無
- 重量：暫無
- 所屬分類：>>
變分分析 本書特色
《變分分析》從該理論的*初起源——積分函數的*小化開始，對該理論做了較深的討論。變分觀點的發展很大程度上和優化、平衡、控制這些理論是緊密相關的。書中在一個統一的框架之中，全面講述了經典分析和凸分析之外的變分幾何和次微積分知識。也講述了集收斂、集值映射和epi收斂、對偶和正則被積函數。本書由洛克菲勒著。
變分分析 內容簡介
in this book we aim to present， in a unified framework， a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization， equilibrium， control， and stability of linear and nonlinear systems. the title variational analysis refiects this breadth. for a long time， variational problems have been identified mostly with the 'calculus of variations'. in that venerable subject， built around the minimization of integral functionals， constraints were relatively simple and much of the focus was on infinite-dimensional function spaces. a major theme was the exploration of variations around a point， within the bounds imposed by the constraints， in order to help characterize solutions and portray them in terms of 'variational principles'. notions of perturbation， approximation and even generalized differentiability were extensively investigated， variational theory progressed also to the study of so-called stationary points， critical points， and other indications of singularity that a point might have relative to its neighbors， especially in association with existence theorems for differential equations.
變分分析 目錄
chapter 1. max and min
a. penalties and constraints
b. epigraphs and semicontinuity
c. attainment of a minimum
d. continuity, closure and growth
e. extended arithmetic
f. parametric dependence
g. moreau envelopes
h. epi-addition and epi-multiplication
i*. auxiliary facts and principles
commentary
chapter 2. convexity
a. convex sets and functions
b. level sets and intersections
c. derivative tests
d. convexity in operations
e. convex hulls
f. closures and contimuty
g.* separation
h* relative interiors
i* piecewise linear functions
j* other examples
commentary
chapter 3. cones and cosmic closure
a. direction points
b. horizon cones
c. horizon functions
d. coercivity properties
e* cones and orderings
f* cosmic convexity
g* positive hulls
commentary
chapter 4. set convergence
a. inner and outer limits
b. painleve-kuratowski convergence
c. pompeiu-hausdorff distance
d. cones and convex sets
e. compactness properties
f. horizon limits
g* contimuty of operations
h* quantification of convergence
i* hyperspace metrics
commentary
chapter 5. set-valued mappings
a. domains, ranges and inverses
b. continuity and semicontimuty
c. local boundedness
d. total continuity
e. pointwise and graphical convergence
f. equicontinuity of sequences
g. continuous and uniform convergence
h* metric descriptions of convergence
i* operations on mappings
j* generic continuity and selections
commentary .
chapter 6. variational geometry
a. tangent cones
b. normal cones and clarke regularity
c. smooth manifolds and convex sets
d. optimality and lagrange multipliers
e. proximal normals and polarity
f. tangent-normal relations
g* recession properties
h* irregularity and convexification
i* other formulas
commentary
chapter 7. epigraphical limits
a. pointwise convergence
b. epi-convergence
c. continuous and uniform convergence
d. generalized differentiability
e. convergence in minimization
f. epi-continuity of function-valued mappings
g. continuity of operations
h* total epi-convergence
i* epi-distances
j* solution estimates
commentary
chapter 8. subderivatives and subgradients
a. subderivatives of functions
b. subgradients of functions
c. convexity and optimality
d. regular subderivatives
e. support functions and subdifferential duality
f. calmness
g. graphical differentiation of mappings
h* proto-differentiability and graphical regularity
i* proximal subgradients
j* other results
commentary
chapter 9. lipschitzian properties
a. single-valued mappings
b. estimates of the lipschitz modulus
c. subdifferential characterizations
d. derivative mappings and their norms
e. lipschitzian concepts for set-valued mappings
……
chapter 10. subdifferential calculus
chapter 11. dualization
chapter 12. monotone mappings
chapter 13. second-order theory
chapter 14. measurability
a. penalties and constraints
b. epigraphs and semicontinuity
c. attainment of a minimum
d. continuity, closure and growth
e. extended arithmetic
f. parametric dependence
g. moreau envelopes
h. epi-addition and epi-multiplication
i*. auxiliary facts and principles
commentary
chapter 2. convexity
a. convex sets and functions
b. level sets and intersections
c. derivative tests
d. convexity in operations
e. convex hulls
f. closures and contimuty
g.* separation
h* relative interiors
i* piecewise linear functions
j* other examples
commentary
chapter 3. cones and cosmic closure
a. direction points
b. horizon cones
c. horizon functions
d. coercivity properties
e* cones and orderings
f* cosmic convexity
g* positive hulls
commentary
chapter 4. set convergence
a. inner and outer limits
b. painleve-kuratowski convergence
c. pompeiu-hausdorff distance
d. cones and convex sets
e. compactness properties
f. horizon limits
g* contimuty of operations
h* quantification of convergence
i* hyperspace metrics
commentary
chapter 5. set-valued mappings
a. domains, ranges and inverses
b. continuity and semicontimuty
c. local boundedness
d. total continuity
e. pointwise and graphical convergence
f. equicontinuity of sequences
g. continuous and uniform convergence
h* metric descriptions of convergence
i* operations on mappings
j* generic continuity and selections
commentary .
chapter 6. variational geometry
a. tangent cones
b. normal cones and clarke regularity
c. smooth manifolds and convex sets
d. optimality and lagrange multipliers
e. proximal normals and polarity
f. tangent-normal relations
g* recession properties
h* irregularity and convexification
i* other formulas
commentary
chapter 7. epigraphical limits
a. pointwise convergence
b. epi-convergence
c. continuous and uniform convergence
d. generalized differentiability
e. convergence in minimization
f. epi-continuity of function-valued mappings
g. continuity of operations
h* total epi-convergence
i* epi-distances
j* solution estimates
commentary
chapter 8. subderivatives and subgradients
a. subderivatives of functions
b. subgradients of functions
c. convexity and optimality
d. regular subderivatives
e. support functions and subdifferential duality
f. calmness
g. graphical differentiation of mappings
h* proto-differentiability and graphical regularity
i* proximal subgradients
j* other results
commentary
chapter 9. lipschitzian properties
a. single-valued mappings
b. estimates of the lipschitz modulus
c. subdifferential characterizations
d. derivative mappings and their norms
e. lipschitzian concepts for set-valued mappings
……
chapter 10. subdifferential calculus
chapter 11. dualization
chapter 12. monotone mappings
chapter 13. second-order theory
chapter 14. measurability
展開全部
變分分析 作者簡介
R. Tyrrell Rockafellar, Roger J-B Wets是國際知名學者，在數學和物理學界享有盛譽。本書凝聚了作者多年科研和教學成果，適用于科研工作者、高校教師和研究生。
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