A Morse-Theoretic Approach to Non-Convex Optimization
Abstract
Non-convex optimization is becoming the foundation for a wide range of applications in modern engineering. Examples include deep learning, signal processing, robotics, autonomy, and numerous others. The class of non-convex problems is broader than the class of convex problems, and the extensive impact of convex optimization suggests the theory of non-convex optimization is poised to match or surpass that impact. However, non-convex optimization remains poorly understood. Many standard analyses for convex problems do not carry over to the non-convex setting, and the analysis of non-convex optimization algorithms is often ad-hoc or heuristic (if done at all). Stronger theoretical guarantees are not only desirable in academic and industrial research, but they are also a pre-requisite for the deployment of neural networks and other technologies in realworld safety-critical systems. To enable novel, rigorous performance guarantees, this YIP project will establish new connections between Morse theory and non-convex optimization. Optimization algorithms will be studied as dynamical systems, and convergence to minimizers will be analyzed as stability.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 29, 2024
- Source ID
- FA95502310120
Entities
People
- Matthew Hale
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Florida