Browsing by Author

  • Publication
    Equilibrium Problems: Existence Results and Applications
    (Springer Science and Business Media B.V., 2018)
    COTRINA ASTO, JOHN EDWIN
    ;
    GARCIA RAMOS, YBOON VICTORIA
    In this paper, we introduce certain regularizations for bifunctions, based on the corresponding regularization for functions, originally defined by J-P. Crouzeix. We show that the equilibrium problems associated to a bifunction and its regularizations are equivalent in the sense that they share the same solution set. Also, we introduce new existence results for the Equilibrium Problem, and we show some applications to minimization and Nash equilibrium problems. © 2017, Springer Science+Business Media B.V.
    Scopus© Citations 12
  • Publication
    Integration formulas via the Fenchel subdifferential of nonconvex functions
    ( 2012-02-01)
    Correa R.
    ;
    García Y.
    ;
    Hantoute A.
    Starting from explicit expressions for the subdifferential of the conjugate function, we establish in the Banach space setting some integration results for the so-called epi-pointed functions. These results use the ε- subdifferential and the Fenchel subdifferential of an appropriate weak lower semicontinuous (lsc) envelope of the initial function. We apply these integration results to the construction of the lsc convex envelope either in terms of the ε-subdifferential of the nominal function or of the subdifferential of its weak lsc envelope. © 2011 Elsevier Ltd. All rights reserved.
  • Publication
    Single-directional property of multivalued maps and variational systems
    ( 2009-12-01)
    Aussel D.
    ;
    Garcia Y.
    ;
    Hadjisavvas N.
    Dontchev and Hager [Math. Oper. Res., 19 (1994), pp. 753-768] have shown that a monotone set-valued map defined from a Banach space to its dual which satisfies the Aubin property around a point (x, y) of its graph is actually single-valued in a neighborhood of x. We prove a result which is the counterpart of the above for quasi-monotone set-valued maps, based on the concept of single-directional property. As applications, we provide sufficient conditions for this single-valued property to hold for the solution map of general variational systems and quasi-variational inequalities. We also investigate the single-directionality property for the normal operator to the sublevel sets of a quasi-convex function. © 2009 Societ y for Industrial and Applied Mathematics.