Linear Programming

Linear programming (LP) is a mathematical method for achieving the best outcome (such as maximum profit or lowest cost) in a given mathematical model whose requirements are represented by linear relationships. Current research emphasizes enhancing LP's capabilities through hybrid approaches combining it with machine learning, particularly for handling complex, real-world problems and improving the efficiency of solving large-scale instances. This includes developing novel algorithms like those based on gradient flows, and leveraging large language models to automate problem formulation and solution. The impact of these advancements is significant, improving the efficiency and applicability of LP across diverse fields, from resource allocation and logistics to machine learning hyperparameter tuning and even AI explainability.