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

作者：Jeyakumar V^*; Li G

来源：Operations Research Letters, 2015, 43(4): 405-410.

DOI：10.1016/j.orl.2015.05.006

• Bilevel programming
• Global polynomial optimization
• Bilevel Farkas' lemma
• Semidefinite programming

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.

• 出版日期2015-7