Quasiconvex programming with locally starshaped constraint region and applications to quasiconvex MPEC

In this article we prove an existence result, necessary and sufficient conditions for quasiconvex programming problem with a locally starshaped constraint region. Our optimality conditions are different from the usual optimality conditions, in that the subdifferential of the objective function is replaced by a normal cone operator. Such an optimality condition has advantage over the usual one, i.e. it becomes sufficient even when the objective function is only quasiconvex. As a special case we derive the corresponding results for the class of 'Quasiconvex-quasiaffine' MPEC which is a class of mathematical programs with complementarity constraints where the objective function is quasiconvex, the inequality constraint is quasiconvex and the rest of constraints are quasiaffine.