Advanced optimization methods for power systems

Power system planning and operation offers multitudinous
opportunities for optimization methods. In practice,
these problems are generally large-scale, non-linear, subject to
uncertainties, and combine both continuous and discrete variables.
In the recent years, a number of complementary theoretical
advances in addressing such problems have been obtained in the
field of applied mathematics. The paper introduces a selection of
these advances in the fields of non-convex optimization, in mixedinteger
programming, and in optimization under uncertainty.
The practical relevance of these developments for power systems
planning and operation are discussed, and the opportunities for
combining them, together with high-performance computing and
big data infrastructures, as well as novel machine learning and
randomized algorithms, are highlighted.