OptNet is a neural network architecture that integrates optimization problems, specifically quadratic programs (QPs), as individual layers within deep networks. These layers encode complex constraints and dependencies that traditional layers cannot capture. The paper presents a framework where each layer's output is the solution to an optimization problem based on the previous layer. This allows for richer representation and end-to-end training for complex tasks requiring inference. The paper develops an efficient solver for these layers using a primal-dual interior point method, which can solve batches of QPs much faster than existing solvers like Gurobi and CPLEX. This solver provides backpropagation gradients with minimal additional cost. The authors demonstrate the effectiveness of OptNet in learning hard constraints, such as in a mini-Sudoku game, where the network learns the rules from input and output examples without prior knowledge. OptNet layers are shown to be subdifferentiable everywhere and differentiable almost everywhere, making them suitable for neural network training. The paper also highlights the representational power of OptNet layers, showing they can approximate arbitrary piecewise-linear functions and outperform traditional layers in certain tasks. However, the method has limitations, including computational complexity and the need for careful tuning. Experimental results demonstrate that OptNet layers are computationally more expensive than linear layers but still tractable for many practical applications. The method is shown to improve upon existing convex optimization techniques in signal denoising and to learn complex constraints in Sudoku problems. The paper concludes that OptNet provides a new primitive for neural networks, enabling end-to-end learning of optimization problems.OptNet is a neural network architecture that integrates optimization problems, specifically quadratic programs (QPs), as individual layers within deep networks. These layers encode complex constraints and dependencies that traditional layers cannot capture. The paper presents a framework where each layer's output is the solution to an optimization problem based on the previous layer. This allows for richer representation and end-to-end training for complex tasks requiring inference. The paper develops an efficient solver for these layers using a primal-dual interior point method, which can solve batches of QPs much faster than existing solvers like Gurobi and CPLEX. This solver provides backpropagation gradients with minimal additional cost. The authors demonstrate the effectiveness of OptNet in learning hard constraints, such as in a mini-Sudoku game, where the network learns the rules from input and output examples without prior knowledge. OptNet layers are shown to be subdifferentiable everywhere and differentiable almost everywhere, making them suitable for neural network training. The paper also highlights the representational power of OptNet layers, showing they can approximate arbitrary piecewise-linear functions and outperform traditional layers in certain tasks. However, the method has limitations, including computational complexity and the need for careful tuning. Experimental results demonstrate that OptNet layers are computationally more expensive than linear layers but still tractable for many practical applications. The method is shown to improve upon existing convex optimization techniques in signal denoising and to learn complex constraints in Sudoku problems. The paper concludes that OptNet provides a new primitive for neural networks, enabling end-to-end learning of optimization problems.