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.

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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

sandwich theorem, Lewis — Ralph      153
sandwich theorem, Lewis — Ralph      153
sandwiched functions      151
sandwiched functions      151
sandwiched functions      151
Schatten p-spaces      326
Schatten p-spaces      326
Schatten p-spaces      326
Segment      15
Segment      15
Segment      15
Self-adjoint operator      317
Self-adjoint operator      317
Self-adjoint operator      317
Sensitivity      65
Sensitivity      65
Sensitivity      65
Separable      139
Separable      139
Separable      139
Separable points      259
Separable points      259
Separable points      259
separable reduction      245 247 249
separable reduction      245 247 249
separable reduction      245 247 249
Separation theorem      132 209
Separation theorem      132 209
Separation theorem      132 209
sequence of sets upper limit      169
sequence of sets upper limit      169
sequence of sets, lower limit      169
sequence of sets, lower limit      169
sequence of sets, lower limit      169
sequence of sets, Painlev $\' e$ — Kuratowski limit      169
sequence of sets, Painlev $\' e$ — Kuratowski limit      169
sequence of sets, Painlev $\' e$ — Kuratowski limit      169
sequential uniform lower semicontinuity      73
sequential uniform lower semicontinuity      73
Set-valued function      3
Set-valued function      3
sgn      76
Shadow price      264 265
Shadow price      264 265
Sign function      76
Sign function      76
Sign function      76
singular subdifferential      196 294
singular subdifferential, Clarke      191
singular subdifferential, Clarke      191
singular subdifferential, Clarke      191
singular value largest      78
singular value largest      78
Slice      266 267
Slice      266 267
Slice      266 267
slice weak-star      266
slice weak-star      266
slice weak-star      266
smooth chain rule      296
smooth chain rule      296
smooth chain rule      296
Solvability      97 229
Solvability      97 229
Spectral decomposition      306
Spectral decomposition      306
Spectral decomposition      306
Spectral function      38 299 302
Spectral function      38 299 302
Spectral function      38 299 302
Spectral radius      302
Spectral radius      302
Spectral radius      302
Spectral sequence      317
Spectral sequence      317
Spectral sequence      317
spectral sequence space      318
spectral sequence space      318
spectral sequence space      318
Stab      293
Stability      90
Stability      90
Stabilizer      293
Stabilizer      293
Stabilizer      293
Stable set      89
Stable set      89
Stable set      89
star of a set      213
star of a set      213
star of a set      213
Stegall variational principel      238 267
Stiemke's theorem      28
Stiemke's theorem      28
Strictly convex      124
Strictly convex      124
Strictly convex      124
strictly convex and Hessian      124
strictly convex and Hessian      124
strictly convex and Hessian      124
Strong minimum      33 267
Strong minimum      33 267
Strong minimum      33 267
strongly exposed      271
strongly exposed      271
strongly exposed      271
strongly exposing functional      271
strongly exposing functional      271
strongly exposing functional      271
Subadditive      118
Subadditive      118
Subadditive      118
Subderivative      39
Subderivative      39
subderivative, proximal      45
subderivative, proximal      45
subderivative, superderivative representation      101
subderivative, superderivative representation      101
subderivative, superderivative representation      101
Subdifferentiable      39
Subdifferential      39
Subdifferential      39
subdifferential at optimality      117
subdifferential at optimality      117
subdifferential at optimality      117
subdifferential density      297
subdifferential density      297
subdifferential density      297
subdifferential of convex functions      117
subdifferential of convex functions      117
subdifferential of infimum      230
subdifferential of infimum      230
subdifferential of infimum      230
subdifferential of max function      94
subdifferential of max function      94
subdifferential of max function      94
subdifferential on manifolds      294
subdifferential on manifolds      294
subdifferential on manifolds      294
Subdifferential, Clarke      189
Subdifferential, convex      117
Subdifferential, convex      117
subdifferential, Fr $\' e$ chet      294
subdifferential, Fr $\' e$ chet      294
subdifferential, Fr $\' e$ chet      294
subdifferential, G $\^ a$ teaux      331
subdifferential, G $\^ a$ teaux      331

subdifferential, G $\^ a$ teaux      331
subdifferential, limiting      196 294
subdifferential, limiting      196 294
subdifferential, limiting      196 294
subdifferential, limiting and Clarke      196
subdifferential, limiting and Clarke      196
subdifferential, limiting and Clarke      196
subdifferential, monotonicity      167
subdifferential, monotonicity      167
subdifferential, monotonicity      167
subdifferential, nonempty      121
subdifferential, nonempty      121
subdifferential, nonempty      121
subdifferential, proximal      45
subdifferential, proximal      45
subdifferential, proximal      45
subdifferential, singular      196 294
subdifferential, singular      196 294
subdifferential, singular      196 294
subdifferential, spectral function      307 311
subdifferential, spectral function      307 311
subdifferential, spectral function      307 311
subgradient and normal cone      130
subgradient and normal cone      130
subgradient and normal cone      130
subgradient construction of      120
subgradient construction of      120
subgradient construction of      120
subgradient existence of      120
subgradient existence of      120
subgradient of maximum eigenvalue      123
subgradient of maximum eigenvalue      123
subgradient of maximum eigenvalue      123
subgradient of norm      123
subgradient of norm      123
subgradient unique      121
subgradient unique      121
subgradient unique      121
sublevel sets      3 166
sublevel sets, normal cone representation      58
sublevel sets, normal cone representation      58
sublevel sets, normal cone representation      58
sublevel sets, singular normal cone representation      61
Sublinear      118 120 132
Sublinear      118 120 132
Submanifold      292
Submanifold      292
Submanifold      292
sum rule, convex sub differential      129 132
sum rule, convex sub differential      129 132
sum rule, convex sub differential      129 132
sum rule, limiting      189 197
sum rule, limiting      189 197
sum rule, limiting      189 197
sum rule, local      54 57
sum rule, local      54 57
sum rule, nonlocal      48
sum rule, nonlocal      48
Sun      219
Sun      219
Sun      219
superderivative, subderivative representation      100
Superdifferential      294
Supergradient      294
supp $\phi$       33
Support      33
Support      33
Tangent bundle      292
Tangent bundle      292
Tangent bundle      292
Tangent cone      209
Tangent cone      209
Tangent cone      209
tangent cone, Clarke      190
tangent cone, Clarke      190
tangent cone, Clarke      190
Tangent space      292
Tangent space      292
Tangent space      292
tangent space, bases of      292
tangent space, bases of      292
tangent space, bases of      292
Tangent vectors      291
Tangent vectors      291
Tangent vectors      291
tr(a)      302
Trace      302
Trace      302
Trace      302
Trace class operators      317
Trace class operators      317
Transversality      185 240
ubiquitous set      191
ubiquitous set      191
ubiquitous set      191
Unit ball      2
Unit ball      2
Unit ball      2
Unitary equivalent      318
Unitary equivalent      318
Unitary equivalent      318
Unitary invariant      302 318
Unitary mapping      302
Unitary operator      318
Unitary operator      318
Unitary operator      318
Upper semicontinuous      44
Upper semicontinuous      44
Upper semicontinuous      44
usco      174
usco      174
usco      174
usco minimal      174
Value function      127
Value function      127
Value function      127
Variational Principle      2 35
Variational Principle      2 35
Variational Principle      2 35
variational principle in finite dimensional spaces      19
variational principle in finite dimensional spaces      19
variational principle in finite dimensional spaces      19
variational principle smooth      19
variational principle, Borwein — Preiss      30 40 42 48 51
variational principle, Borwein — Preiss      30 40 42 48 51
variational principle, Borwein — Preiss      30 40 42 48 51
variational principle, Deville — Godefroy — Zizler      33
variational principle, Deville — Godefroy — Zizler      33
variational principle, Deville — Godefroy — Zizler      33
variational principle, Ekeland      6 8 10 12 14 16 17 59 131 194 255 277
variational principle, one-perturbation      281
variational principle, one-perturbation      281
variational principle, one-perturbation      281
variational principle, Stegall      238 267
variational principle, subdifferential form      42
Variational techniques      1
Vector field      292
Ville's theorem      28
Viscosity solution      50
viscosity solution uniqueness      51
Viscosity subsolution      50
Viscosity supersolution      50
viscosity, Fr $\' e$ chet subderivative      39
viscosity, Fr $\' e$ chet subdifferential      39
von Neumann — Theobald inequality      306 308
w*-lim $_{i \to \infty}\ x_i^*$       193
welfare economy      263
Yosida approximate      183

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