A decomposition strategy for decision problems with endogenous uncertainty using mixed-integer programming

Decision problems under endogenous uncertainty are still challenging to solve, despite the advances in solution methods and increasing computational power. A novel framework called Decision Programming solves such decision problems using off-the-shelf solvers by using influence diagrams to represent decision problems with decision-dependent probabilities, and then converting the influence diagram representation of the problem to … Read more

An enhanced L-Shaped method for optimizing periodic-review inventory control problems modeled via two-stage stochastic programming

This paper presents the development of an enhanced L-Shaped method applied to an inventory management problem that considers a replenishment control system based on the periodic review (R,S) policy. We consider single-item one-echelon problems with uncertain demands and partial backorder that are modeled using two-stage stochastic programming. To enable the consideration of large-scale problems, the … Read more

A parallelizable augmented Lagrangian method applied to large-scale non-convex-constrained optimization problems

We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is compact but not necessarily convex. Such problems arise, for example, in the split-variable deterministic reformulation of stochastic mixed-integer optimization problems. The dual solution approach needs … Read more

Combining Penalty-based and Gauss-Seidel Methods for solving Stochastic Mixed-Integer Problems

In this paper, we propose a novel decomposition approach for mixed-integer stochastic programming (SMIP) problems that is inspired by the combination of penalty-based Lagrangian and block Gauss-Seidel methods (PBGS). In this sense, PBGS is developed such that the inherent decomposable structure that SMIPs present can be exploited in a computationally efficient manner. The performance of … Read more

Combining Progressive Hedging with a Frank-Wolfe Method to Compute Lagrangian Dual Bounds in Stochastic Mixed-Integer Programming

We present a new primal-dual algorithm for computing the value of the Lagrangian dual of a stochastic mixed-integer program (SMIP) formed by relaxing its nonanticipativity constraints. The algorithm relies on the well-known progressive hedging method, but unlike previous progressive hedging approaches for SMIP, our algorithm can be shown to converge to the optimal Lagrangian dual … Read more