《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。

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