Feasible Set

A feasible set represents the collection of permissible solutions or states within a given system, subject to constraints. Current research focuses on efficiently computing and utilizing feasible sets in diverse applications, including optimization problems (like vehicle routing and online convex optimization), robotics (wrench capacity and legged locomotion), and fair machine learning. This involves developing algorithms that leverage the curvature of feasible sets to improve efficiency and guarantee constraint satisfaction, often employing techniques like linear optimization oracles, convex hull methods, and multi-level optimization. Understanding and manipulating feasible sets is crucial for improving the performance and robustness of algorithms across various fields.