On the existence of solutions to generalized quasi-equilibrium problems

In this paper, we apply new results on variational relation problems obtained by D. T. Luc (J Optim Theory Appl 138:65–76, 2008 ) to generalized quasi-equilibrium problems. Some sufficient conditions on the existence of its solutions of generalized quasi-equilibrium problems are shown. As special ca...

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Bibliographic Details
Published inJournal of global optimization Vol. 52; no. 4; pp. 711 - 728
Main Authors Duong, Truong Thi Thuy, Tan, Nguyen Xuan
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.04.2012
Springer Nature B.V
Subjects
Applied mathematics
Computer Science
Equilibrium
Hypotheses
Mapping
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Studies
Quasi-optimization problems
pseudomonotone
Generalized quasi-equilibrium problems
90C48
Upper and lower
strong pseudomonotone multivalued mappings
Upper and lower-quasiconvex-like multivalued mappings
49J53
continuous multivalued mappings
Upper and lower quasivariational inclusions
quasiconvex
49J27
91B50
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Summary:In this paper, we apply new results on variational relation problems obtained by D. T. Luc (J Optim Theory Appl 138:65–76, 2008 ) to generalized quasi-equilibrium problems. Some sufficient conditions on the existence of its solutions of generalized quasi-equilibrium problems are shown. As special cases, we obtain several results on the existence of solutions of generalized Pareto and weak quasi-equilibrium problems concerning C -pseudomonotone multivalued mappings. We deduce also some results on the existence of solutions to generalized vector Pareto and weakly quasivariational inequality and vector Pareto quasi-optimization problems with multivalued mappings.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-011-9700-7