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Hu S., Papageorgiou N.S. — Handbook of Multivalued Analysis, Volume II: Applications
Hu S., Papageorgiou N.S. — Handbook of Multivalued Analysis, Volume II: Applications

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Название: Handbook of Multivalued Analysis, Volume II: Applications

Авторы: Hu S., Papageorgiou N.S.

Аннотация:

This is the second of a two-volume exposition on the theory and applications of set-valued maps. Multivalued analysis is a remarkable mixture of many different fields of mathematics, such as topology, measure theory, nonlinear functional analysis and applied mathematics. This two-volume work provides a comprehensive survey of the general theory and applications of set-valued analysis. The existing books on the subject deal with either one particular domain of the subject or present primarily the finite dimensional aspects of the theory and applications. In contrast these volumes give a complete picture of the subject, both from the theoretical and applied viewpoints, including important new developments that have occurred in recent years and a detailed bibliography.
The present volume presents the applications of the theory of set-valued maps, which include various kinds of evolution inclusions, differential inclusions, integral inclusions, optimal control, calculus of variations, mathematical economics, game theory and optimization. Although the presentation of these applications assumes some knowledge of mathematical analysis, the authors have made every effort, including the addition of an appendix, to keep the work self-contained.
Audience: This work is an essential reference for graduate students and researchers interested in the applications of multivalued analysis, such as mathematicians working on differential and evolution inclusions, control theorists, mathematical economists, game theorists and people working on optimization and calculus variations.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 918

Добавлена в каталог: 05.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$R_{\delta}$-set      49
$\delta$-normal economy      614
$\delta$-productive      620
$\Gamma$-regularization      405 545
$\Gamma$-relaxation      405
$\Gamma_{seq}$-limits of sequences      416
$\theta$-optimal policy      762
$\varepsilon$-optimal policy      746
$\varepsilon$-optimal strategy      713
a-topology      632
Absolute retract      49
Absolutely continuous      797
Action space      719
Adaptive control model      753
Adjoint semigroup      482
Admissible control      355
Admissible ordinary control      378
Admissible plan      793
Admissible policy      744
Admissible relaxed control      378
Admissible state      355
Admissible state-control pair      355
Admissible topology      277
Affine continuous      846
Approximate controllability      486
Approximate local null controllability      497
Approximate null controllability      489
Arbitrage opportunity      677
Asymptotically discount optimal      754
Average reward criterion      731
Average turnpike property      609
b-convergence      524
b-feasible program      603
Bang-bang property      226
Bary center      414
Base of a cone      855
Bellman’s inequality      239
Bellman’s principle of optimality      720
Biting lemma      524
Boundedly order complete      854
Budget set      691
C-compact      862
C-convex      858
C-saturated      854
c-topology      832
Cabb — Douglas production function      636
Cadlag-process      674
Capital accumulation program      631
Caratheodory’s convexity theorem      404
CES-production function      636
Chain rule      865
Chebyshev center      218
Chebyshev radius      218
Choquet function      27
Coalation      686
Compact-open topology      632
Competitive (Walras) equiblirium      686
Competitive allocation      830
Competitive contract      830
Competitive price      830
Competitive program      618 646
Complementarity problem      375
Concave multifunction      575
Condition (C)      532
Conjugate functional      566
Constraint qualification      608
Consumption sequence      617
Continuous transition probability      708
Continuous-time dynamic progr.      743
Contractible set      50
Controllability operator      482
Controlled Markov process      729
Core      686
Cournot — Nash equiblirium distrib.      784
Cournot — Nash equilibrium      771
Critical point      308
Cut-off function      536
Daniell otvs      854
Deformation Lemma      310
Demand set      691
Deterministic policy      761
Differential variational inequality      196
Dirac distribution      864
Directed downward      340
Directed upward      340
Directional continuity ($\Gamma$-continuity)      208
Dirichlet problem      242
discount factor      603 632
Discount optimal policy      754
Discounted golden rule stock      612
Discounted reward criterion      754
Discrepancy function      756 763
Discrete probability measure      379
Discrete-time dynamic programming      719
Distribution (vector valued)      864 867
Distributional derivative      864
Distributions      864
Doeblin’s hypothesis      787
Dual cone      856
Dual problem      847
Dynamic programming equation      721 756
Dynamic programming operator      736 755
Effective domain      567
Ekeland variational principle      447
Empirical process      756
Epi-convergence      555
Equiconvergent in measure      808
Equilibrium      829
Equilibrium pair      725
Ergodicity conditions      734
Estimation problem      226
EU-rational      840 842
Evolution operator      272 285
Evolution triple      3
Ex ante dominated      840 842
Ex ante mixture dominated      844
Exact controllability      479
Expansible stock      622
Extremal solutions      340
Extremely desirable bundle      689
Feasible allocation      827
Feasible program      597
Feasible s-program      624
Feedback policy      730
Filtering problem      225
Filtration      674
First eigenvalue      318 322
Free disposability      607
G-convergence      86
Galerkin method      9
Game      780
Gelfand integral      377
Generalized directional derivative      308
Generalized function      864
Generalized plan      795
Generalized pseudo-Hamiltonian      662
Girsanov’s theorem      677
Good program      598 609
Gronwall inequality      239
Growth condition $C_{p}$      519
Growth condition of order $1\leq p\leq \infty$      540
Hamiltonian function      448 630
Hausdorff measure of noncompactness      210
Improve upon      686
Improved upon      829
Inada conditions      636
Indifference relation      692
Integral representation      540
Integral solution      251
Integration by parts formula      4
Interpolation inequality      7
Invariant probability      71
Kuratowski measure of noncompac.      210
L-generalized pseudomonotone      40
L-pseudomonotone      40
Lavrentiev phenomenon      530
Leray — Schauder principle      231 346
Linear quadratic problem      660
Ljusternik — Schnirelman theory      322
Local martingale      676
Local on S      540
Locally Lipschitz      307
Locally Lipschitz boundary      863
Lottery      837
Lower solution      332
Lower value function      713
M-integrand      556
Mackey topology      638
Marginals      779
Markov game      714
Markov policy      719 730 744
McKenzie competitive program      663
Measure of noncompactness      210
Measure of weak noncompactness      344
Measure on S      540
Memoryless policy      730
Method of auxiliary variable      407
Metric likelihood      211
Mild solution      267 297
Min max character, of eigenvalues      322
Minimal hypersurface problem      529
Modulus of uniform equicontinuity      757
Mountain Pass Theorem      311
Multiple $\Gamma$-operators      405
Multiple $\Gamma$-sequential limits      405
Multivalued eigenvalue problem      246
Mutually singular      797
N-measurability      313
Narrow topology      378 707
Navier — Stokes equation      187
Neumann problem      242
Nonstationary value iteration (NVI)      759
Normal problem      567
Null-controllability      489
One sector model      636
Optimal discounted return function      746
Optimal pair      355
Optimal policy      720 746
Optimal program      617
Optimal reward function      731
Optimal stationary program      621
Optimal strategy      713
Optimal value function      754
Optimality equation      732
Optional $\sigma$-field      675
Order convex      854
Ordered tvs (otvs)      854
Original controls      378
Orthogonal      495
p-equilibrium pair      725
p-Laplacian      322
Palais — Smale condition      308
Parabolic variational inequalities      370
Parameter estimation problem      365
Pareto efficient      854
Pareto minimal      854
Partial ordering      853
Path      597
Penalty function      333
Periodic Problem      242
Poincare inequality      866
Poincare — Wirtinger inequality      866
Policy      719 730 754
Policy improvement algorithm      750
Polyconvex      589
Portmanteau theorem      708 778
Prediction problem      225
Preference relation      692
Price system      638
Primal problem      847
Principle of estimation and control      758
PROGRAM      597
Property Q      354
Property U      108
Proportionately expansible      622
Pseudoinverse      482
Public good      703
q-admissible plan      793
q-generalized plan      795
q-optimal plan      795
Quasi-affine      550
Quasi-convex      517
Quasi-minimizers      417
Quasi-optimal elements      417
Radon measure      778 867
Rank-one convex      589
Rayleigh quotient      322
Reachable set      297
Realizable allocation      827
Realizable contract configuration      829
Reduction technique      353
Relaxable problem      438
Relaxed functional      409
Relaxed problem      437
Resolvent convergence      283
Resolvent operator      487
Resolvent set      487
Restriction      797
Retractive representation      147
Reward function      719
s-period valuation      625
Saddle point theorem      312
Scorza Dragoni directional continuity      208
Section of A      854
Semigroup convergence      265
Set of $\varepsilon$-minimizers      560
Set of finite codimension      444
Set of minimizers      560
Set of s-feasible capital stocks      625
Setwise convergence      739
singular      797
Singular functional      638
Singularly achieved      800
Slater condition      608
Sobolev space (vector valued)      6
Space criterion      17
Span contraction      737
Span fixed point      737
Span seminorm      737
Stable problems      567
State space      711 719 729 743 754
Stationary deterministic policy      761
Stationary policy      754
Stationary price support      620
Stationary program      620
Stochastic dominance      838
Stochastic game      723
Stochastic kernel      708
Strategy      712
Strong derivative      302
Strong invariance      66
Strong maximality      597
Strong relaxation      25
Strong solution      116
Strong topology      722
Strongly equiconvergent      808
Subdifferential (convex)      567
Subdifferential (in the sense of Clarke)      308
Subgradient      567
Sufficient input vector      619
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