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

Maximal monotone      167 177
maximal monotone on a set      176
maximum eigenvalue      302
Meager      33
Mean value inequality      102
Mean value inequality      102
Mean value inequality      102
mean value theorem approximate      81
mean value theorem Cauchy      84
mean value theorem Lagrange      79
mean value theorem Lagrange      79
mean value theorem Lagrange      79
mean value theorem Rolle      79
mean value theorem Rolle      79
mean value theorem Rolle      79
metric regularity      234 236 239
metric regularity      234 236 239
metric regularity, tangential conditions      240
Metric space      2
minimal cusco      177 202 215
minimal cusco      177 202 215
minimal cusco      177 202 215
minimal usco      175
minimal usco      175
minimal usco, existence      175
minimal usco, existence      175
minimal usco, existence      175
Minimax theorem      99 139
Minimax theorem      99 139
Minimax theorem      99 139
minimizer subdifferential zeroes      117
monotone maximal      167
Monotone multifunction      166
Monotone multifunction      166
Monotone multifunction      166
monotone quasi      83
monotone quasi      83
monotone quasi      83
Monotonicity      79
Monotonicity      79
Monotonicity      79
monotonicity cone      83
monotonicity cone      83
monotonicity cone      83
monotonicity of gradients      125
Mountain Pass Theorem      274 278
mountain pass theorem approximate      276
mountain pass theorem approximate      276
mountain pass theorem approximate      276
multidirectional mean value inequality      95 231 253
multidirectional mean value inequality      95 231 253
multidirectional mean value inequality      95 231 253
multidirectional mean value inequality approximate      95
multidirectional mean value inequality approximate      95
multidirectional mean value inequality approximate      95
multidirectional mean value inequality convex      130
multidirectional mean value inequality convex      130
multidirectional mean value inequality convex      130
multidirectional mean value inequality refined      102
multidirectional mean value inequality refined      102
multidirectional mean value inequality refined      102
multidirectional mean value inequality two sets      153
multidirectional mean value inequality two sets      153
multidirectional mean value inequality two sets      153
Multifunction      3 165 233
multifunction argmin      166
multifunction argmin      166
multifunction argmin      166
multifunction close valued      166
multifunction close valued      166
multifunction close valued      166
multifunction closed      166
multifunction closed      166
multifunction compact valued      166
multifunction compact valued      166
multifunction composition      222
multifunction continuity      173
multifunction continuity      173
multifunction continuity      173
multifunction convex valued      166
multifunction convex valued      166
multifunction convex valued      166
multifunction domain of      4 165
multifunction domain of      4 165
multifunction domain of      4 165
multifunction epigraphical profile      166
multifunction epigraphical profile      166
multifunction epigraphical profile      166
multifunction graph of      3 165
multifunction inverse of      4 165
multifunction maximal monotone      167 176
multifunction monotone      166
multifunction monotone boundedness      168
multifunction monotone boundedness      168
multifunction monotone boundedness      168
multifunction open valued      166
multifunction open valued      166
multifunction open valued      166
multifunction profile mapping      174
multifunction profile mapping      174
multifunction profile mapping      174
multifunction range of      165
multifunction range of      165
multifunction range of      165
multifunction semicontinuity      173
multifunction semicontinuity      173
multifunction semicontinuity      173
multifunction sequential lower limit      173
multifunction sequential lower limit      173
multifunction sequential lower limit      173
multifunction sequential upper limit      173
multifunction sequential upper limit      173
multifunction sequential upper limit      173
multifunction subdifferential      165
multifunction subdifferential      165
multifunction subdifferential      165
multifunction sublevel set mapping      174
multifunction sublevel sets      166
Multiobjective optimization      106
Multiplier set      65
multipliers nonexistence      76
Nearest point      140 150
nearest point existence and uniqueness      140
nearest point in polyhedron      139
nearest point normal cone characterization      141
Necessary optimality condition      68 198
necessary optimality condition approximate multiplier rule      62 64
necessary optimality condition Clarke subdifferential      190
necessary optimality condition comparison      211
necessary optimality condition Fr $\' e$ chet normal cone condition      41
necessary optimality condition Frizt John condition      64
necessary optimality condition Guignard      241
necessary optimality condition Karush — Kuhn — Tucker      67 68 70 77
necessary optimality condition, Lagrange multiplier rule      211 212 298
necessary optimality condition, multi-objective optimization      107
necessary optimality condition, Pshenichnii — Rockafellar      131 141
nonconvex separation theorem      259
nonconvex separation theorem and extremal principle      262
nonconvex separation theorem for multifunctions      259
nonconvex separation theorem for sets      261
Nonexpansive function      217
Nonexpansive mapping      179
nonexpansive mapping extension      179
nonlocal approximate sum rule      48 51 55 95 105 128 253 260
Nonsmooth analysis      2
nonsymmetrical minimax theorem      99 103
norm, subgradients of      123
normal cone, and subgradients      130
normal cone, Clarke      190
normal cone, convex      117

normal cone, epigraph      42
normal cone, Fr $\' e$ chet      41
normal cone, level sets      60
normal cone, limiting      196
normal cone, nonclosed      201
normal cone, of a submanifold      295
normal cone, on manifolds      294
normal cone, sublevel sets      58
normal cone, to intersection      130
normal upper semicontinuity      265
one-perturbation variational principle      281
open covering with a linear rate      234
Open mapping theorem      114
Open mapping theorem      114
optimal principle      53
optimal principle      53
optimal principle      53
optimal value dual      135
optimal value dual      135
optimal value dual      135
Optimal value function      54 65
optimal value primal      135
optimal value primal      135
optimal value primal      135
Optimality condition      189
optimization constrained      62 190
optimization constrained      62 190
optimization constrained      62 190
optimization multiobjective      106
optimization multiobjective      106
optimization multiobjective      106
optimization multiobjective, necessary optimality conditions      107
optimization multiobjective, necessary optimality conditions      107
optimization multiobjective, necessary optimality conditions      107
optimization, subdifferential in      117
optimization, subdifferential in      117
optimization, subdifferential in      117
Orbit      293 306
Orbit      293 306
order statistic function      312
order statistic function      312
order statistic function      312
Order-reversing      134
Pacman set      210
Pacman set      210
Pacman set      210
Painlev $\' e$ Kuratowski limit      169
Painlev $\' e$ Kuratowski limit      169
Painlev $\' e$ Kuratowski limit      169
paired Banach spaces      318
paired Banach spaces      318
paired Banach spaces      318
Palais — Smale condition      278
Palais — Smale condition      278
Pareto optimal allocation      264
Pareto optimal allocation      264
Pareto optimal allocation      264
PASS      275
PASS      275
Permutation invariant      302
Permutation matrix      22 302
Permutation matrix      22 302
Pitt's theorem      272
polar      190
polar      190
Polar cone      136
Polar cone      136
Polyhedron      133
polyhedron, nearest point in      139
polyhedron, nearest point in      139
polyhedron, nearest point in      139
Positive operator      317
Positive operator      317
Positively homogeneous      118
Positively homogeneous      118
pr $_{\eta}(S; v)$       232
preference      106
preference      106
preference      106
preferred neighborhood      292
preferred neighborhood      292
preferred neighborhood      292
Preimage      3
Preimage      3
Preimage      3
Projection      141
Projection algorithm      143
projection algorithm asymptotically regular      145
projection algorithm asymptotically regular      145
projection algorithm asymptotically regular      145
projection algorithm convergence      145
projection algorithm convergence      145
projection algorithm strong convergence      148
projection algorithm strong convergence      148
projection algorithm strong convergence      148
projection algorithm weak convergence      147
projection algorithm weak convergence      147
projection, algorithm      143
projection, algorithm      143
projection, algorithm      143
projection, approximate      232
projection, approximate      232
projection, attractive property      143
projection, attractive property      143
projection, attractive property      143
projection, potential function of      141
projection, potential function of      141
projection, properties      141
proximal normal cone      218
proximal normal formula      218
proximal normal vector      218
proximal sub derivative      45
proximal subdifferential      45
pseudo convex set      211
pseudo convex set      211
pseudo-Lipschitzian      234
pseudo-Lipschitzian      234
pseudo-Lipschitzian      234
Pseudotangent cone      209
Pshenichnii — Rockafellar conditions      131
quasi convexity      83 167
quasi monotone      83
Radon — Nikodym property      267 271
range F      165
real normed sequence space      317
real normed sequence space      317
real normed sequence space      317
Rearrangement      319
Rearrangement      319
Rearrangement      319
rearrangement equivalent      318
rearrangement equivalent      318
rearrangement equivalent      318
Rearrangement invariant      319
regularity function      192
regularity function      192
regularity function      192
regularity set      210
regularity set      210
regularity set      210
Residual      33
Residual      33
Residual      33
Resolvent      183
Resolvent      183
Resolvent      183
s-lim inf $_{x \to \overline{x}}\ F(x)$       173
s-lim sup $_{x \to \overline{x}}\ F(x)$       173
Sandwich theorem      127 128
sandwich theorem, Lewis — Ralph      153

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