Bilevel aggregator-prosumers' optimization problem in real-time:A convex optimization approach

This paper proposes a Real-Time Market (RTM) platform for an aggregator and its corresponding prosumers to participate in the electricity wholesale market. The proposed energy market platform is modeled as a bilevel optimization problem where the aggregator and the prosumers are considered as self-interested agents. We present a convex optimization problem which can capture a subset of the set of global optima of the bilevel problem as its optimal solution

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