Akul Bansal

SDDmiP.jl: A Software Package with a Provably Convergent Benders Algorithm for Multi-Stage Stochastic Mixed-Integer Programming

Categories Optimization Software and Modeling Systems, Stochastic Programming Tags , , , , , ,

We present an open-source software package that implements a provably convergent Benders-type decomposition algorithm for multistage stochastic integer programs. In addition to standard cut families, such as Benders, strengthened Benders, and Lagrangian cuts, the algorithm incorporates rectified linear unit (ReLU) cuts, which provide convergence guarantees for general mixed-integer state variables. However, the dual problems used … Read more

Normalization of ReLU Dual for Cut Generation in Stochastic Mixed-Integer Programs

Categories Stochastic Programming Tags , ,

We study the Rectified Linear Unit (ReLU) dual, an existing dual formulation for stochastic programs that reformulates non-anticipativity constraints using ReLU functions to generate tight, non-convex, and mixed-integer representable cuts. While this dual reformulation guarantees convergence with mixed-integer state variables, it admits multiple optimal solutions that can yield weak cuts. To address this issue, we … Read more

A computational study of cutting-plane methods for multi-stage stochastic integer programs

Categories Stochastic Programming Tags , ,

We report a computational study of cutting plane algorithms for multi-stage stochastic mixed-integer programming models with the following cuts: (i) Benders’, (ii) Integer L-shaped, and (iii) Lagrangian cuts. We first show that Integer L-shaped cuts correspond to one of the optimal solutions of the Lagrangian dual problem, and, therefore, belong to the class of Lagrangian … Read more