The Solution Existence of Equilibrium Problems and Generalized Problems

  • Nguyen Xuan Hai

    Student thesis: Doc typesDoctor of Sciences


    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.
    Date of Award2007
    Original languageEnglish
    SupervisorPhan Quoc Khanh (Supervisor), Jean-Jacques STRODIOT (Jury), Jean-Paul Penot (Jury) & The Luc Dinh (Jury)


    • Equilibrium problems
    • existence of solutions

    Cite this