  In this paper we begin by discussing the simple bilevel programming problem
(SBP) and its extension the simple mathematical programming problem under
equilibrium constraints (SMPEC). Here we first define both these problems and
study their interrelations. Next we study the various types of necessary and
sufficient optimality conditions for the (SMPEC) problems; which occur under
various reformulations. The optimality conditions for the (SBP) problem are
special cases of the results obtained here when the lower level objective is
the gradient of a convex function. Among the various optimality conditions
presented here are the sequential optimality conditions, which do not need any
constraint qualification. We also present here a schematic algorithm for the
(SMPEC) problem, where the sequential optimality conditions play a key role in
the convergence analysis.
