作者：R.TyrrellRockafell
页数：734
出版社：世界图书出版公司
出版日期：2013
ISBN：9787510061363
电子书格式：pdf/epub/txt
内容简介
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.
作者简介
R. Tyrrell Rockafellar, Roger J-B Wets是国际知名学者，在数学和物理学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。
本书特色
《变分分析》从该理论的最初起源——积分函数的最小化开始，对该理论做了较深的讨论。变分观点的发展很大程度上和优化、平衡、控制这些理论是紧密相关的。书中在一个统一的框架之中，全面讲述了经典分析和凸分析之外的变分几何和次微积分知识。也讲述了集收敛、集值映射和epi收敛、对偶和正则被积函数。本书由洛克菲勒著。
目录
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最. 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.最 separation
h最 relative interiors
i最 piecewise linear functions
j最 other examples
commentary
chapter 3. cones and cosmic closure
a. direction points
b. horizon cones
c. horizon functions
d. coercivity properties
e最 cones and orderings
f最 cosmic convexity
g最 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最 contimuty of operations
h最 quantification of convergence
i最 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最 metric descriptions of convergence
i最 operations on mappings
j最 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最 recession properties
h最 irregularity and convexification
i最 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最 total epi-convergence
i最 epi-distances
j最 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最 proto-differentiability and graphical regularity
i最 proximal subgradients
j最 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
