Several notes on Lagrangian Relaxation for unit commitment

Lagrangian Relaxation (LR) based algorithms are among the most successful methods for unit commitment (UC) and short term hydro-thermal scheduling. In this paper, some important problems related to LR are studied and summarized. Such problems include the possibility of positive duality gap, the difference between relative and absolute duality gap, and economical interpretation of the optimal multipliers, and so on. The results obtained can be viewed as relevant addition to LR for UC and are useful to lead to a better understanding of the nature of LR.