Dual Feasible Solution

Dual feasible solutions are a focus of current optimization research, aiming to efficiently find solutions that satisfy both primal and dual problem constraints. Researchers are exploring machine learning approaches, including deep learning and augmented Lagrangian methods, to predict dual solutions directly or improve the convergence of iterative algorithms like column generation and interior-point methods. This work is significant because accurate dual solutions provide valuable certificates of optimality and can accelerate the solution of large-scale optimization problems across diverse fields, such as power systems and machine learning model training. Improved methods for constructing "safe" regions containing the dual solution are also actively being developed to enhance screening tests and improve efficiency.