KKT-Informed Neural Network

TL;DR

A neural network-based approach for solving parametric convex optimization problems is presented, where the network estimates the optimal points given a batch of input parameters, enabling parallel solving of a class of optimization problems.

Abstract

A neural network-based approach for solving parametric convex optimization problems is presented, where the network estimates the optimal points given a batch of input parameters. The network is trained by penalizing violations of the Karush-Kuhn-Tucker (KKT) conditions, ensuring that its predictions adhere to these optimality criteria. Additionally, since the bounds of the parameter space are known, training batches can be randomly generated without requiring external data. This method trades guaranteed optimality for significant improvements in speed, enabling parallel solving of a class of optimization problems.

Figures (5)

• Figure 1: Feasibile set $\mathcal{D}$
• Figure 2: Loss terms during training
• Figure 3: MAE
• Figure 4: $R^{2}$
• Figure 6: Computation time comparison