  Microgrids are increasingly being utilized to improve the resilience and
operational flexibility of power grids, and act as a backup power source during
grid outages. However, it necessitates that the microgrid itself could provide
power to the critical loads. This paper presents an algorithm named alternating
optimization based sequential boolean quadratic programming tailored for
solving optimal demand shut-offs problems arising in microgrids. Moreover, we
establish local superlinear convergence of the proposed approximate Boolean
quadratic programming method over nonconvex problems. In the end, the
performance of the proposed method is illustrated on the modified IEEE 30-bus
case study.
