J. M. Borwein, Qi.Zhu — Techniques of Variational Analysis (CMS Books in Mathematics) :: Электронная библиотека попечительского совета мехмата МГУ

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J. M. Borwein, Qi.Zhu — Techniques of Variational Analysis (CMS Books in Mathematics)

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Название: Techniques of Variational Analysis (CMS Books in Mathematics)

Авторы: J. M. Borwein, Qi.Zhu

Аннотация:

Variational arguments are classical techniques whose use can be traced back to the early development of the calculus of variations and further. Rooted in the physical principle of least action, they have wide applications in diverse fields. This book provides a concise account of the essential tools of infinite-dimensional first-order variational analysis. These tools are illustrated by applications in many different parts of analysis, optimization and approximation, dynamical systems, mathematical economics and elsewhere. Much of the material in the book grows out of talks and short lecture series given by the authors in the past several years. Thus, chapters in this book can easily be arranged to form material for a graduate level topics course. A sizeable collection of suitable exercises is provided for this purpose. In addition, this book is also a useful reference for researchers who use variational techniques - or just think they might like to.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель без номеров страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 366

Добавлена в каталог: 30.04.2020

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Предметный указатель

epi-limit lower      170
epi-limit upper      171
Epigraph of function      3
epigraphical profile      166
exact penalization      38
Ext      29
extremal and convex separation      209
extremal approximate      104 107
extremal geometry      106
extremal limiting      199
Extremal point      104
Extremal principle      104
extremal system      104
extremal system fixed sets      108
Extreme points      29
Farkas lemma      29
Feasible allocation      263
Fej $\' e$ r Monotone sequence      144
Fenchel biconjugate      137
Fenchel conjugate      134 152 324
Fenchel conjugate examples      138
Fenchel conjugate of exponential      137 139
Fenchel conjugate transformations      138
Fenchel duality      136 157
Fenchel duality linear constraints      139
Fenchel duality symmetric      139
Fenchel problem      135
Fenchel — Rockafellar Theorem      121
Fenchel — Young inequality      135 137
Fitzpatrick function      177
Fixed point      15
fixed point theorem Banach      15
fixed point theorem Caristi — Kirk      17
fixed point theorem Caristi — Kirk and Banach      18
fixed point theorem Clarke's refinement      16
fixed point theorem error estimate      18
fixed point theorem iteration method      18
flower peta theorem      11
flower petal      11
Fr $\' e$ chet coderivative      220
Fr $\' e$ chet derivative      39
Fr $\' e$ chet differentiable      39 243
Fr $\' e$ chet normal cone      41
Fr $\' e$ chet smooth space      39
Fr $\' e$ chet sub derivative      39
Fr $\' e$ chet subdifferentiable      39
Fr $\' e$ chet subdifferential      39 245
Fr $\' e$ chet super derivative      98
Fr $\' e$ chet superdifferential      44 50 98
Fritz John condition      64
Function characteristic      45
function convex, Lipschitz property      112
function convex, regularity      192
Function, bump      33
Function, Cantor      45
Function, distance      3 38 150 214 230
function, eigenvalue      38 312
Function, entropy      158
Function, entropy      158
Function, entropy      158
function, epigraph of      3
function, epigraph of      3
function, epigraph of      3
function, Fitzpatrick      177
function, Fitzpatrick      177
function, Fitzpatrick      177
Function, gauge      111
function, gauge-type      30
function, gauge-type      30
function, gauge-type      30
Function, graph of      3
Function, graph of      3
Function, graph of      3
Function, indicator      3
Function, indicator      3
Function, indicator      3
function, indicator conjugate of      139
function, indicator subdifferential of      117
Function, Lipschitz      38 79
function, lower semicontinuous (lsc)      2 3
function, lower semicontinuous (lsc)      2 3
function, lower semicontinuous (lsc)      2 3
Function, Lyapunov      88 89
function, max      37
function, max      37
function, max      37
function, max subdifferential of      133
function, max subdifferential of      133
function, max subdifferential of      133
Function, nonexpansive      217
Function, nonexpansive      217
Function, nonexpansive      217
function, number of elements      23
function, number of elements      23
function, number of elements      23
Function, optimal value      37 53
function, order statistic      312
function, order statistic      312
function, penalization      38
function, penalization      38
function, penalization      38
function, set of continuity      120
function, set of continuity      120
Function, sign      76
Function, spectral      38
Function, spectral      38
Function, support      111 162
Function, support      111 162
Function, support      111 162
G $\^ a$ teaux differentiable      10 121
Game      109
Game      109
Game      109
gauge-type function      30
gauge-type function      30
gauge-type function      30
general metric regularity qualification condition      223
general metric regularity qualification condition      223
general metric regularity qualification condition      223
GENERIC      33
GENERIC      33
GENERIC      33
generic G $\^ a$ teaux differentiability      287
generic G $\^ a$ teaux differentiability      287
generic G $\^ a$ teaux differentiability      287
Gordan alternative      20
Gordan alternative      20
Gordan alternative      20
Graph      3
graph F      3
Graph of function      3
Graves — Lyusternik thoerem      103
Graves — Lyusternik thoerem      103
Hadamard's inequality      78
Hadamard's inequality      78
Hadamard's inequality      78
Hahn — Banach extension      132
Hahn — Banach extension      132
Hahn — Banach extension      132
Hamilton — Jacobi equation      50 53
Hamilton — Jacobi equation      50 53
Hamilton — Jacobi equation      50 53
Hessian and convexity      124
Hessian and convexity      124
Hessian and convexity      124
hypermonotone      182
hypermonotone      182
hypermonotone      182
Implicit function theorem      233
Implicit function theorem      233

Implicit function theorem      233
implicit multifunction      233
implicit multifunction      233
implicit multifunction      233
Indicator function      3
Indicator function      3
Indicator function      3
Induced map      292
Induced map      292
Induced map      292
Inf-convolution      3 149
int S      3
Interior      3
Interior      3
Interior      3
Kirszbraun — Valentine theorem      179
Kirszbraun — Valentine theorem      179
Kirszbraun — Valentine theorem      179
Kronecker delta      317
Ky Fan minimax theorem      303
Ky Fan minimax theorem      303
Ky Fan minimax theorem      303
Lagrange multiplier rule      212 298
Lagrange multiplier rule      212 298
Lagrange multiplier rule      212 298
Lambert W-function      150
Lambert W-function      150
Lambert W-function      150
Level sets      3
Level sets      3
Level sets      3
level sets normal cone representation      60
level sets of majorization      21
level sets of majorization      21
level sets of majorization      21
level sets of preference      107
level sets of preference      107
level sets of preference      107
level sets, singular normal cone, representation      61
level sets, singular normal cone, representation      61
level sets, singular normal cone, representation      61
Lexicographic order      319
Lexicographic order      319
Lexicographic order      319
Lidskii theorem      317
Lidskii theorem      317
Lidskii theorem      317
Lie bracket      299
Lie bracket      299
Lie bracket      299
Lie group      293
Lie group      293
Lie group      293
Lie group action      293
lim inf $_{i \to \infty}\ F_i$       169
lim sup $_{i \to \infty}\ F_i$       169
lim $_{i \to \infty}\ F_i$       169
limiting chain rule      198
limiting chain rule      198
limiting chain rule      198
limiting coderivative      220
limiting coderivative      220
limiting extremal principle      199
limiting multiplier rule      198
limiting multiplier rule      198
limiting multiplier rule      198
limiting normal cone      196
limiting normal cone      196
limiting normal cone      196
limiting subdifferential      196 294
limiting subdifferential      196 294
limiting sum rule      197
limiting sum rule      197
limiting sum rule      197
limiting sum rule failure      200
limiting sum rule failure      200
Linearity space      118
Linearity space      118
Linearity space      118
Lipschitz and cone monotonicity      86
Lipschitz and cone monotonicity      86
Lipschitz and cone monotonicity      86
Lipschitz criterion      82
Lipschitz criterion      82
Lipschitz criterion      82
Lipschitz property      79
Local coordinate system      291
local sum rule      253
local sum rule      253
local sum rule      253
local sum rule approximate      54 57 62 87 102 107 252
local sum rule approximate      54 57 62 87 102 107 252
local sum rule approximate      54 57 62 87 102 107 252
LOG      139
LOG      139
LOG      139
Lower semicompact      226
Lower semicompact      226
Lower semicompact      226
lower semicontinuous (lsc)      3
lower semicontinuous (lsc)      3
lower semicontinuous (lsc)      3
lsc closure      52
lsc closure      52
lsc closure      52
Lyapunov function      89
Lyapunov function      89
Lyapunov function      89
Lyapunov majorizatio and doubly stochastic matrix      26
Lyapunov majorizatio and doubly stochastic matrix      26
Lyapunov majorizatio level sets of      21 27
Lyapunov majorizatio level sets of, representation      22
Lyapunov majorization      21
Lyapunov majorization      21
Lyapunov majorization      21
Lyapunov stability      89
Lyapunov stability      89
Lyapunov stability      89
Mangasarian — Fromovitz condition      67
Manifold      291
Manifold      291
Manifold      291
manifold full rank matrices      299
manifold invertible matrices      299
manifold orthogonal matrices      299
manifold Stiefel      301
mapping attracting      143
Mapping nonexpansive      143
marginal price rule      206
marginal price rule      206
marginal price rule      206
Mathematical economics      206
Mathematical economics      206
Mathematical economics      206
mathematical program with equilibrium constraint      77
mathematical program with equilibrium constraint      77
mathematical program with equilibrium constraint      77
Matrix      299
matrix doubly stochastic      23 159
matrix doubly stochastic      23 159
Matrix permutation      22
Matrix permutation      22
Matrix permutation      22
matrix skew symmetric      299
matrix skew symmetric      299
matrix skew symmetric      299
Matrix symmetric      299
max formula      120
max formula      120
max formula      120

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