Optima and equilibria: new inner regularizations

Jacqueline Morgan, M.B. Lignola (University of Naples Federico II)

First, for a family of parametric minimum or equilibrium problems, we present new possible "inner regularizations" requiring, among other conditions, the lower semicontinuity of the approximation solution maps. Then, we propose corresponding concepts of "viscosity solutions" for bilevel problems (more precisely optimization or Minsup problems with constraints defined by a parametric minimum or equilibrium problem) for which existence of solutions, and/or nice asymptotic behavior of solutions under perturbations of the data, is not guaranteed.