Lagrangian Dual Decision Rules for Multistage Stochastic Mixed-Integer Programming

Multistage stochastic programs can be approximated by restricting policies to follow decision rules. Directly applying this idea problems with integer decisions is difficult because of the need for rules that lead integral decisions. In work, we introduce Lagrangian dual (LDDRs) multistage mixed-integer programming (MSMIP) which overcome difficulty in a MSMIP. We propose two new bounding techniques based on stagewise (SW) and nonanticipative (NA) duals where multiplier are restricted LDDRs. demonstrate how solutions from these used drive primal policies. Our proposal requires fewer assumptions than most existing MSMIP methods. compare theoretical strength show NA provide relaxation bounds at least as good ones obtained SW dual. our numerical study problem classes, one traditional novel, observe proposed LDDR approaches yield significant optimality gap reductions compared general-purpose methods problems.