Andrew J. Schaefer Strong relaxations are critical for solving deterministic mixed-integer programs. As solving stochastic mixed-integer programs (SMIPs) is even harder, it is likely that strong relaxations will also prove essential for SMIPs. We consider general two-stage SMIPs with recourse, where integer variables are allowed in both stages of the problem and randomness is allowed in the objective … Read more
Outer linearization methods for two-stage stochastic linear programs with recourse, such as the L-shaped algorithm,generally apply a single optimality cut on the nonlinear objective at each major iteration, while the multicut version of the algorithm allows for several cuts to be placed at once. In general, the L-shaped algorithm tends to have more major iterations … Read more
Inverse optimization perturbs objective function to make an initial feasible solution optimal with respect to perturbed objective function while minimizing cost of perturbation. We extend inverse optimization to two-stage stochastic linear programs. Since the resulting model grows with number of scenarios, we present two decomposition approaches for solving these problems. Citation Unpublished: 07-1, University of … Read more
We consider totally unimodular stochastic programs, that is, stochastic programs whose extensive-form constraint matrix is totally unimodular. We generalize the notion of total unimodularity to apply to sets of matrics and provide properties of such sets. Using this notion, we give several sufficient conditions for specific classes of problems. When solving such problems using the … Read more