The Benders by batch algorithm: Design and stabilization of an enhanced algorithm to solve multicut Benders reformulation of two-stage stochastic programs

A decomposition method for distributionally-robust two-stage stochastic mixed-integer conic programs

“…In line with the work [11], this paper also aims to improve the efficiency of generating Lagrangian cuts for solving tsSMIP with the strategy of 'cut generation in batches'. Note that this strategy has been proved valid in generating Benders cuts [6] for solving two-stage stochastic linear programs through numerical experiments. The convergence of Bender decomposition is thus accelerated significantly.…”

“…Based on these facts, we try to generate Lagrangian cuts in batches for tsSMIP, and thereby to enhance the efficiency of improving the lower bound of the Bender master problem of (1.5). Compared with the work in [6], our algorithm tackles the situation of Lagrangian relaxation, and thus undergoes a more intricate convergence property analysis. In addition, we highlight a robust theoretical result that emphasizes the superiority of our proposed method.…”