Finite-Dimensional Variational Inequalities and Complementarity Problems

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Springer Science & Business Media, Jun 4, 2007 - Business & Economics - 704 pages
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The ?nite-dimensional nonlinear complementarity problem (NCP) is a s- tem of ?nitely many nonlinear inequalities in ?nitely many nonnegative variables along with a special equation that expresses the complementary relationship between the variables and corresponding inequalities. This complementarity condition is the key feature distinguishing the NCP from a general inequality system, lies at the heart of all constrained optimi- tion problems in ?nite dimensions, provides a powerful framework for the modeling of equilibria of many kinds, and exhibits a natural link between smooth and nonsmooth mathematics. The ?nite-dimensional variational inequality (VI), which is a generalization of the NCP, provides a broad unifying setting for the study of optimization and equilibrium problems and serves as the main computational framework for the practical solution of a host of continuum problems in the mathematical sciences. The systematic study of the ?nite-dimensional NCP and VI began in the mid-1960s; in a span of four decades, the subject has developed into a very fruitful discipline in the ?eld of mathematical programming. The - velopments include a rich mathematical theory, a host of e?ective solution algorithms, a multitude of interesting connections to numerous disciplines, and a wide range of important applications in engineering and economics. As a result of their broad associations, the literature of the VI/CP has bene?ted from contributions made by mathematicians (pure, applied, and computational), computer scientists, engineers of many kinds (civil, ch- ical, electrical, mechanical, and systems), and economists of diverse exp- tise (agricultural, computational, energy, ?nancial, and spatial).
 

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Contents

IV
xxiii
V
xxv
VI
624
VII
625
VIII
626
IX
638
X
656
XI
661
LIX
966
LX
969
LXI
975
LXII
978
LXIII
981
LXIV
989
LXV
991
LXVI
993

XII
663
XIII
674
XIV
686
XV
692
XVI
703
XVII
708
XVIII
715
XIX
723
XX
724
XXI
736
XXII
739
XXIII
753
XXIV
757
XXV
764
XXVI
766
XXVII
771
XXVIII
786
XXIX
788
XXX
793
XXXI
794
XXXII
798
XXXIII
809
XXXIV
816
XXXV
822
XXXVI
826
XXXVII
833
XXXVIII
839
XXXIX
844
XL
852
XLI
857
XLII
865
XLIV
866
XLV
869
XLVI
877
XLVII
882
XLVIII
891
XLIX
892
LI
909
LII
912
LIII
913
LIV
921
LV
930
LVI
939
LVII
947
LXVII
996
LXVIII
1000
LXIX
1003
LXXI
1006
LXXII
1012
LXXIII
1016
LXXIV
1022
LXXV
1031
LXXVI
1036
LXXVII
1043
LXXVIII
1053
LXXIX
1060
LXXX
1072
LXXXI
1078
LXXXII
1084
LXXXIII
1092
LXXXIV
1097
LXXXV
1107
LXXXVI
1108
LXXXVII
1115
LXXXVIII
1119
LXXXIX
1125
XC
1133
XCI
1135
XCIII
1141
XCIV
1147
XCVI
1153
XCVII
1164
XCVIII
1165
XCIX
1171
C
1176
CI
1178
CII
1180
CIII
1183
CIV
1184
CV
1187
CVI
1204
CVII
1209
CVIII
1214
CIX
1222
CX
1235
CXI
1273
CXII
1278
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Page 1271 - Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan...
Page 630 - A complex-valued function on [a, b] is in fiip^fa, &]) [see the definition in (17.31)] if and only if for every e > 0 there is a <5 > 0 such that for all sequences ([ah, &*])"=,! of subintervals of [a, b] for which Z (b, -<*)<* k=i holds, the inequality holds. That is, / is "absolutely continuous with overlap permitted".

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About the author (2007)

Jong-Shi Pang was awarded the 2003 Dantzig Prize, the worlds top prize in the area of Mathematical Programming.

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