Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/existence-theory-for-finite-dimensional-pseudomonotone-equilibrium-9VNzgWssoq
References (59)
-
J. Yao (1994)
Variational Inequalities with Generalized Monotone OperatorsMath. Oper. Res., 19
-
A. Auslender, P. Coutat (1994)
On closed convex sets without boundary rays and asymptotesSet-Valued Analysis, 2
-
K. Fan (1961)
A generalization of Tychonoff's fixed point theoremMathematische Annalen, 142
-
N. Hadjisavvas, S. Schaible (1998)
From Scalar to Vector Equilibrium Problems in the Quasimonotone CaseJournal of Optimization Theory and Applications, 96
-
R. Rockafellar, R. Wets (1986)
A Lagrangian Finite Generation Technique for Solving Linear-Quadratic Problems in Stochastic Programming -
J. Gwinner (1978)
On the Existence and Approximation of Solutions of Pseudomonotone Variational Inequalities -
G. Yuan, G. Isac, K. Tan, Jian Yu (1998)
The Study of Minimax Inequalities, Abstract Economics and Applications to Variational Inequalities and Nash EquilibriaActa Applicandae Mathematica, 54
-
Monica Bianchi, S. Schaible (1996)
Generalized monotone bifunctions and equilibrium problemsJournal of Optimization Theory and Applications, 90
-
P. Harker, J. Pang (1990)
Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applicationsMathematical Programming, 48
-
I. Ekeland, R. Téman (1976)
Convex analysis and variational problems -
J. Crouzeix (1997)
Pseudomonotone variational inequality problems: Existence of solutionsMathematical Programming, 78
-
N. Hadjisavvas, S. Schaible (1998)
Generalized Convexity, Generalized Monotonicity: Recent Results -
G. Mastroeni (2003)
Gap Functions for Equilibrium ProblemsJournal of Global Optimization, 27
-
A. Auslender (2000)
Existence of optimal solutions and duality results under weak conditionsMathematical Programming, 88
-
P. Ruíz-Canales, A. Rufián-Lizana (1995)
A characterization of weakly efficient pointsMathematical Programming, 68
-
G. Mastroeni (1999)
Minimax and extremum problems associated to a variational inequality, 58
-
R. W. Cottle, J. S. Pang, R. E. Stone (1992)
The Linear Complementarity Problem -
E. Blum, W. Oettli (1994)
From optimization and variational inequalities to equilibrium problems, 63
-
J. Gwinner (1981)
On fixed points and variational inequalities—a circular tourNonlinear Analysis-theory Methods & Applications, 5
-
H. Brezis, L. Nirenberg, G. Stampacchia (1972)
A remark on Ky Fan's minimax principleBoll. Unione Mat. Ital., 6
-
W. Oettli (1997)
A remark on vector-valued equilibria and generalized monotonicity -
S. Adly, D. Goeleven, M. Théra (1996)
Recession mappings and noncoercive variational inequalitiesNonlinear Analysis-theory Methods & Applications, 26
-
E. Belousov, D. Klatte (2002)
A Frank–Wolfe Type Theorem for Convex Polynomial ProgramsComputational Optimization and Applications, 22
-
Fabián Bazán, Fernando Flores-Bazán (2003)
Vector Equilibrium Problems Under Asymptotic AnalysisJournal of Global Optimization, 26
-
A. Auslender, P. Coutat (1994)
Closed convex sets without rays and asymptotesSet-Valued Anal., 2
-
S. Karamardian (1976)
Complementarity problems over cones with monotone and pseudomonotone mapsJournal of Optimization Theory and Applications, 18
-
F. Flores-Bazán (2003)
Radial Epiderivatives and Asymptotic Functions in Nonconvex Vector OptimizationSiam Journal on Optimization, 14
-
N. Hadjisavvas, S. Schaible (1998)
Quasimonotonicity and Pseudomonotonicity in Variational Inequalities and Equilibrium Problems -
J. Dedieu (1979)
Cônes asymptotes d'ensembles non convexes, 60
-
A. Auslender (2000)
Existence of optimal solutions and duality results under minimal hypothe-sisMath. Programming, 88
-
H. Attouch, Z. Chbani, A. Moudafi (1994)
Recession Operators and Solvability of Vari-ational Problems in Reflexive Banach Spaces -
J. Gwinner (1978)
Optimization and Operation Research -
D. Kinderlehrer, G. Stampacchia (1980)
An introduction to variational inequalities and their applications -
R. T. Rockafellar, R. J. Wets (1998)
Variational Analysis -
G. Isac, V. Kalashnikov (2001)
Exceptional Family of Elements, Leray–Schauder Alternative, Pseudomonotone Operators and ComplementarityJournal of Optimization Theory and Applications, 109
-
F. Flores-Bazán (2000)
Existence Theorems for Generalized Noncoercive Equilibrium Problems: The Quasi-Convex CaseSiam Journal on Optimization, 11
-
S. Karamardian (1970)
Generalized complementarity problemJournal of Optimization Theory and Applications, 8
-
J. Aubin (1979)
Mathematical methods of game and economic theory -
H. Kuhn (1969)
Duality in Mathematical Programming -
R. Cottle, J. Yao (1992)
Pseudo-monotone complementarity problems in Hilbert spaceJournal of Optimization Theory and Applications, 75
-
J. Guo, J. Yao (1994)
Variational inequalities with nonmonotone operatorsJournal of Optimization Theory and Applications, 80
-
F. Flores-Bazán (2002)
Ideal, weakly efficient solutions for vector optimization problemsMathematical Programming, 93
-
F. Flores-Bazán, W. Oettli (2001)
Simplified Optimality Conditions for Minimizing the Difference of Vector-Valued FunctionsJournal of Optimization Theory and Applications, 108
-
M. Moudafi, M. Théra (1999)
Ill-posed Variational Problems and Regularization Techniques -
D. T. Luc (2001)
Existence results for densely pseudomonotone variational inequalitiesJ. Math. Anal. Appl., 254
-
R. T. Rockafellar (1972)
Convex Analysis -
M. Frank, P. Wolfe (1956)
An algorithm for quadratic programmingNaval Research Logistics Quarterly, 3
-
J. Benoist, J. Hiriart-Urruty (1996)
What is the subdifferential of the closed convex hull of a functionSiam Journal on Mathematical Analysis, 27
-
S. Deng (1998)
On Efficient Solutions in Vector OptimizationJournal of Optimization Theory and Applications, 96
-
D. Gale, V. Klee (1959)
Continuous Convex Sets.Mathematica Scandinavica, 7
-
O. Chadli, Z. Chbani, H. Riahi (1998)
Recession methods for equilibrium problems and applications to variational and hemivariational inequalitiesDiscrete and Continuous Dynamical Systems, 5
-
S. Karamardian (1967)
Strictly quasi-convex (concave) functions and duality in mathematical programmingJournal of Mathematical Analysis and Applications, 20
-
A. Daniilidis, N. Hadjisavvas (1999)
Coercivity conditions and variational inequalitiesMathematical Programming, 86
-
J. Joly, U. Mosco (1979)
A propos de l'existence et de la régularité des solutions de certaines inéquations quasi-variationnellesJournal of Functional Analysis, 34
-
C. Baiocchi, G. Buttazzo, F. Gastaldi, F. Tomarelli (1988)
General existence theorems for unilateral problems in continuum mechanicsArchive for Rational Mechanics and Analysis, 100
-
K. Fan (1972)
Inequality III -
A. Maugeri, W. Oettli, D. Schläger (1997)
A flexible form of Wardrop's principle for traffic equilibria with side constraints -
F. Gastaldi, F. Tomarelli (1987)
Some remarks on nonlinear and noncoercive variational inequalities -
J. P. Didieu (1977)
Cône asymptote d'un ensemble non convexe, application à l'optimizationC.R. Acad. Sci. Paris A, 285
- Publisher
- Springer Journals
- Copyright
- Copyright © 2003 by Kluwer Academic Publishers
- Subject
- Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1023/A:1024971128483
- Publisher site
- See Article on Publisher Site
Abstract
This article was originally written to be delivered during a short course, but because of its finite-dimensional setting, it can also be addressed to nonspecialists and those only possessing a basic background on real analysis and mathematical programming. Thus, it should be conceived as an introduction to the existence theory for equilibrium (general optimization) problems including minimization and variational inequality under the assumption of no compactness and possibly having an unbounded solution set. Nevertheless, some of the results that are established here have not appeared elsewhere. Our approach is based on the asymptotic description of the functions and constraint set. In particular, this allows us to give various characterizations of the nonemptiness (and, in another case, boundedness) of the solution set. Several applications to convex problems in mathematical programming are given, along with applications to vector equilibrium problems. A guide to historical references is also provided.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Oct 5, 2004