Large Scale Linear Programming

Large-scale linear programming (LP) focuses on efficiently solving optimization problems with a vast number of variables and constraints, crucial for diverse applications like logistics and finance. Current research emphasizes accelerating LP solution through first-order methods, often enhanced by machine learning techniques such as reinforcement learning and neural networks (e.g., unrolling optimization algorithms into neural networks). These approaches target improved convergence rates in algorithms like column generation and presolve, aiming to reduce computational time and improve the scalability of LP solvers for real-world problems. The resulting advancements have significant implications for various fields by enabling the solution of previously intractable optimization problems.