Homotopy Optimization

Homotopy optimization tackles complex optimization problems by solving a sequence of progressively more difficult surrogate problems, tracing a continuous path from an easily solvable initial problem to the target problem. Current research focuses on applying this framework to diverse fields, including motion planning (using probabilistic and game-theoretic approaches), neural network training (developing homotopy relaxation algorithms and applying it to NeuralODEs), and computer vision (leveraging GPU acceleration for homotopy continuation). This approach offers significant advantages in computational efficiency and the ability to find globally optimal solutions, impacting various domains from robotics and AI to algebraic topology and scientific computing.