On Constrained Mixed-Integer DR-Submodular Minimization

DR-submodular functions encompass a broad class of functions which are generally non-convex and non-concave. We study the problem of minimizing any DR-submodular function, with continuous and general integer variables, under box constraints and possibly additional monotonicity constraints. We propose valid linear inequalities for the epigraph of any DR-submodular function under the constraints. We further provide … Read more

A scalable bounding method for multi-stage stochastic integer programs

Many dynamic decision problems involving uncertainty can be appropriately modeled as multi-stage stochastic programs. However, most practical instances are so large and/or complex that it is impossible to solve them on a single computer, especially due to memory limitations. Extending the work of Sandikci et al. (2013) on two-stage stochastic mixed-integer-programs (SMIPs), this paper develops … Read more