Lagrangian-Integrated L-Shaped Methods for Bi-Parameterized Stochastic Integer Programs
A decomposition approach for two-stage stochastic min-max and min-min mixed-integer programs with bi-parameterized recourse, where first-stage decisions alter both the objective and the feasible region of the second stage. The Lagrangian-integrated L-shaped (L2) method augments the classical L-shaped/Benders scheme with Lagrangian information to guarantee exact solutions for pure-binary first stages, adds a regularization-augmented variant for mixed-binary first stages, and handles distributionally robust problems with decision-dependent, possibly-empty ambiguity sets.
Bi-Parameterized Two-Stage Stochastic Min-Max and Min-Min Mixed Integer Programs Sumin Kang1 and
Introduces bi-parameterized two-stage stochastic mixed-integer programs (BTSPs), a min-max/min-min extension of two-stage stochastic programming in which the first-stage decisions shape both the obje…