A bilevel Farkas lemma to characterizing global solutions of a class of bilevel polynomial programs

We present a form of Farkas’ lemma for bilevel inequality systems and use it to obtain a complete characterization of global solutions of a class of bilevel polynomial programs with lower-level linear programs, where the objective functions of the upper-level polynomial programs are coercive. Consequently, we show that a sequence of optimal values of related semidefinite linear programs converges to the global optimal value of a bilevel polynomial program under suitable conditions.