Monotone Profit

Monotone profit functions, where increasing input leads to increasing output, are central to several optimization problems across diverse fields. Current research focuses on developing efficient algorithms for maximizing such profits under various constraints, including fairness considerations and limited resources, often employing submodular maximization techniques and novel polyhedral characterizations like the α-Core. These advancements are crucial for addressing real-world challenges in areas such as fair resource allocation, online learning, and crowd-funding, where ensuring both efficiency and equitable outcomes is paramount. The development of approximation algorithms and online learning strategies for monotone profit maximization continues to be a significant area of investigation.