Many practical optimization problems are difficult for more than one reason; besides being possibly both nonlinear and combinatorial, they are often also very-large-scale. This is typically due to multiple aspects that each independently increase the size of the model, such as many (complex) systems having to be coordinated to achieve a global target on a (long, and/or with small timesteps) time horizon and subject to (different forms of) uncertainty. The compounded effect of these yield models that are way too large to be solved by monolithic approaches.
CommaLAB has a long-standing tradition in the research of solution methods for very-large-scale optimization problems, with approaches ranging from decomposition methods to ad-hoc heuristics to structured interior-point algorithms. We have released complex and well-engineered software for the solution of the problems arising in the context of decomposition approaches, and even an over-ambitious C++ software framework aimed at representing complex optimization models with multiple nested forms of structure and the corresponding sophisticated solution algorithms. Besides the methodological interest, these have allowed to successfully tackle many applications in different fields such as energy, logistics, and others.