In this paper, we establish existence theorems for bilevel problems with
fixed-point constraints and bilevel problems without fixed-point constraint. The aim
of this paper is to investigate under which conditions the existence of a feasible point
of a bilevel problem can be assumed in advance and under which conditions there
exist minimizers for this type of problems. From this, we establish existence theorems
for mathematical programs with equilibrium constraints and semi-infinite problems.
Journal of Optimization Theory and Applications, 137(1):27-40