Augmented Lagrangian duality – Optimization Online

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

Published: 2026/08/06

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

Exact Augmented Lagrangian Duality for Nonconvex Mixed-Integer Nonlinear Optimization

Published: 2024/07/16, Updated: 2025/12/15

(Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming Augmented Lagrangian duality, exact penalty methods, Mixed-integer nonlinear optimization

In the context of mixed-integer nonlinear problems (MINLPs), it is well-known that strong duality does not hold in general if the standard Lagrangian dual is used. Hence, we consider the augmented Lagrangian dual (ALD), which adds a nonlinear penalty function to the classic Lagrangian function. For this setup, we study conditions under which the ALD … Read more