A new framework to generate Lagrangian cuts in multistage stochastic mixed-integer programming

Based on recent advances in Benders decomposition and two-stage stochastic integer programming we present a new generalized framework to generate Lagrangian cuts in multistage stochastic mixed-integer linear programming (MS-MILP). This framework can be incorporated into decomposition methods for MS-MILPs, such as the stochastic dual dynamic integer programming (SDDiP) algorithm. We show how different normalization techniques … Read more

Applying random coordinate descent in a probability maximization scheme

Gradient computation of multivariate distribution functions calls for considerable effort. A standard procedure is component-wise computation, hence coordinate descent is an attractive choice. This paper deals with constrained convex problems. We apply random coordinate descent in an approximation scheme that is an inexact cutting-plane method from a dual viewpoint. We present convergence proofs and a … Read more

It’s All in the Mix: Wasserstein Machine Learning with Mixed Features

Citation Belbasi R., Selvi A., Wiesemann W. (December 2023) It’s all in the mix: Wasserstein machine learning with mixed features. Preprint. Article Download View It's All in the Mix: Wasserstein Machine Learning with Mixed Features

Cutting plane reusing methods for multiple dual optimizations

We consider solving a group of dual optimization problems that share a core structure: Every primal problem of the group is obtained by the right-hand side variation of constraints in the original primal problem, while the other core part of the original primal problem, such as the objective and the left-hand side of the constraints, … Read more

Recovering Dantzig-Wolfe Bounds by Cutting Planes

Dantzig-Wolfe (DW) decomposition is a well-known technique in mixed-integer programming (MIP) for decomposing and convexifying constraints to obtain potentially strong dual bounds. We investigate cutting planes that can be derived using the DW decomposition algorithm and show that these cuts can provide the same dual bounds as DW decomposition. More precisely, we generate one cut … Read more

A New Dual-Based Cutting Plane Algorithm for Nonlinear Adjustable Robust Optimization

This paper explores a class of nonlinear Adjustable Robust Optimization (ARO) problems, containing here-and-now and wait-and-see variables, with uncertainty in the objective function and constraints. By applying Fenchel’s duality on the wait-and-see variables, we obtain an equivalent dual reformulation, which is a nonlinear static robust optimization problem. Using the dual formulation, we provide conditions under … Read more