A bilevel bottleneck programming problem

This paper studies a bilevel programming problem with linear constraints, and in which the objective functions at both levels are concave bottleneck functions which are to be minimized. The problem is a non-convex programming problem. It is shown that an optimal solution to the problem is attainable at an extreme point of the underlying region. The outer level objective function values are ranked in increasing order until a value is reached, one of the solutions corresponding to which is feasible for the problem. This solution is then the required global optimal solution.