Equilibrium problems proposed by Blum and Oettli (1994) and their
extensions have been attracted the attentions of many mathematicians all
over the world for the last decade. This problem setting proved to contain
many optimization-related problems such as the complementarity problem,
the variational inequality, the ¯xed-point and coincidence-point theorems,
the minimax problem, the Nash equilibrium and the tra±c network prob-
lem. The need of considering the constraint set which depends on the state
variable, pointed out by Bensoussan, Goursat and Lions (1973) for ran-
dom impulse optimal control, let to the extension of equilibrium problems
to quasiequilibrium ones. There had been also several papers on further
extensions of the model to systems of quasiequilibrium problems and qua-
sivariational inclusion problems, when we committed to this topic for our
Thesis four years ago. Among various aspects of study for these problems,
the solution existence has been attracted most e®orts, since this issue lies
in the center of each theory. All these reasonings motivate the topic of
our Thesis. Namely, for equilibrium problems, quasiequilibrium problems,
systems of such problems and for our proposed extended problems, i.e. qua-
sivariational inclusion problems and systems of such problems, we always
study su±cient conditions for the solution existence. Comparisons with re-
cent results in the literature are also provided to show advantages of our
existence conditions. We supply applications to illustrate the generality and
applicability of the results in various particular situations.
la date de réponse | 2007 |
---|
langue originale | Anglais |
---|
Superviseur | Phan Quoc Khanh (Promoteur), Jean-Jacques STRODIOT (Jury), Jean-Paul Penot (Jury) & The Luc Dinh (Jury) |
---|
The Solution Existence of Equilibrium Problems and Generalized Problems
Hai, N. X. (Auteur). 2007
Student thesis: Doc types › Docteur en Sciences