Convex Set

Convex sets are fundamental geometric objects with applications across diverse fields, primarily focusing on optimization problems where solutions lie within a convex region. Current research emphasizes efficient algorithms for finding optimal paths within graphs of convex sets, particularly relevant to robotics and motion planning, often employing techniques like A*, convex programming, and semidefinite programming. These advancements improve the speed and quality of solutions for tasks such as autonomous navigation, trajectory generation, and multi-agent coordination, impacting fields ranging from robotics and computer vision to machine learning and operations research.