  This article continues our study on simple bilevel and simple MPEC problems.
In this article we focus on developing algorithms. We show how using the idea
of a gap function one can represent a simple MPEC as a simple bilevel problem
with non-smooth data. This motivates us first to develop an algorithm for a
simple bilevel problem with non-smooth data and modify the scheme for the same
to develop an algorithm for the simple MPEC problem. We also discuss how the
simple bilevel formulation of a simple MPEC can help us in formulating a
stopping criteria for the simple MPEC problem
