变分分析
变分分析作者:[美] 洛克菲勒 (R.Tyrrell Rockafellar),[美] Roger J-B Wets 著 开 本:24开 书号ISBN:9787510061363 定价:99.0 出版时间:2013-10-01 出版社:世界图书出版公司 |
变分分析 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.
变分分析 目录
chapter 1. max and mina. 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
自然科学 数学 数学分析
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