Scalable Mixed-Integer Optimization with Neural Constraints via Dual Decomposition

The introduction of a dual-decomposition framework for mixed-integer optimization marks a significant advancement in the integration of deep neural networks into decision-making processes. Traditional methods often struggle with scalability, leading to intractable problems as the complexity of neural networks increases. The new approach effectively addresses these challenges by decoupling the optimization problem into a mixed-integer program and a neural network block, allowing each to be solved with the most suitable techniques. This modularity not only maintains efficiency but also allows for flexibility in the choice of neural network architectures, as evidenced by the ability to swap between different types of neural networks without altering the underlying code. The framework's performance is validated through the SurrogateLIB benchmark, demonstrating a remarkable speedup of 120 times compared to the exact Big-M formulation, which is crucial for real-time applications in various f…